Properties

Label 7744.2.a
Level $7744$
Weight $2$
Character orbit 7744.a
Rep. character $\chi_{7744}(1,\cdot)$
Character field $\Q$
Dimension $209$
Newform subspaces $101$
Sturm bound $2112$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 7744 = 2^{6} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7744.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 101 \)
Sturm bound: \(2112\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7744))\).

Total New Old
Modular forms 1128 227 901
Cusp forms 985 209 776
Eisenstein series 143 18 125

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(49\)
\(+\)\(-\)\(-\)\(55\)
\(-\)\(+\)\(-\)\(55\)
\(-\)\(-\)\(+\)\(50\)
Plus space\(+\)\(99\)
Minus space\(-\)\(110\)

Trace form

\( 209 q - 2 q^{5} + 193 q^{9} + O(q^{10}) \) \( 209 q - 2 q^{5} + 193 q^{9} - 10 q^{13} + 6 q^{17} - 16 q^{21} + 179 q^{25} - 10 q^{29} - 18 q^{37} - 2 q^{41} + 26 q^{45} + 157 q^{49} + 14 q^{53} + 6 q^{61} + 12 q^{65} + 32 q^{69} - 2 q^{73} + 153 q^{81} + 28 q^{85} - 6 q^{89} + 32 q^{93} - 10 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7744))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11
7744.2.a.a 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-3\) \(-1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}+6q^{9}-6q^{13}+3q^{15}+\cdots\)
7744.2.a.b 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-3\) \(3\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+3q^{5}-2q^{7}+6q^{9}-9q^{15}+\cdots\)
7744.2.a.c 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-2q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
7744.2.a.d 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-2q^{7}+q^{9}+q^{13}+2q^{15}+\cdots\)
7744.2.a.e 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-2\) \(-1\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+2q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
7744.2.a.f 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-2\) \(-1\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+2q^{7}+q^{9}+q^{13}+2q^{15}+\cdots\)
7744.2.a.g 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-2\) \(3\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+3q^{5}-2q^{7}+q^{9}-5q^{13}+\cdots\)
7744.2.a.h 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-2\) \(3\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+3q^{5}+2q^{7}+q^{9}+5q^{13}+\cdots\)
7744.2.a.i 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-4q^{7}-2q^{9}-2q^{13}+\cdots\)
7744.2.a.j 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-4q^{7}-2q^{9}+4q^{13}+\cdots\)
7744.2.a.k 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}-2q^{9}+4q^{13}+\cdots\)
7744.2.a.l 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-1\) \(-1\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+4q^{7}-2q^{9}-4q^{13}+\cdots\)
7744.2.a.m 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-1\) \(3\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-2q^{7}-2q^{9}-4q^{13}+\cdots\)
7744.2.a.n 7744.a 1.a $1$ $61.836$ \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(3\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-q^{3}+3q^{5}-2q^{9}-3q^{15}+9q^{23}+\cdots\)
7744.2.a.o 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(-1\) \(3\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}+4q^{7}-2q^{9}-2q^{13}+\cdots\)
7744.2.a.p 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(0\) \(-3\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-4q^{7}-3q^{9}-3q^{13}+3q^{17}+\cdots\)
7744.2.a.q 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(0\) \(-3\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-4q^{7}-3q^{9}+3q^{13}-3q^{17}+\cdots\)
7744.2.a.r 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(0\) \(-3\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+4q^{7}-3q^{9}-3q^{13}+3q^{17}+\cdots\)
7744.2.a.s 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(0\) \(-3\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+4q^{7}-3q^{9}+3q^{13}-3q^{17}+\cdots\)
7744.2.a.t 7744.a 1.a $1$ $61.836$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{5}-3q^{9}-4q^{13}-8q^{17}-q^{25}+\cdots\)
7744.2.a.u 7744.a 1.a $1$ $61.836$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{5}-3q^{9}+4q^{13}+8q^{17}-q^{25}+\cdots\)
7744.2.a.v 7744.a 1.a $1$ $61.836$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+2q^{5}-3q^{9}+6q^{13}-2q^{17}-q^{25}+\cdots\)
7744.2.a.w 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}-2q^{9}-4q^{13}+\cdots\)
7744.2.a.x 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}-2q^{9}+4q^{13}+\cdots\)
7744.2.a.y 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(1\) \(-1\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+4q^{7}-2q^{9}-2q^{13}+\cdots\)
7744.2.a.z 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(1\) \(-1\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+4q^{7}-2q^{9}+4q^{13}+\cdots\)
7744.2.a.ba 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(1\) \(3\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-4q^{7}-2q^{9}-2q^{13}+\cdots\)
7744.2.a.bb 7744.a 1.a $1$ $61.836$ \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(3\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q+q^{3}+3q^{5}-2q^{9}+3q^{15}-9q^{23}+\cdots\)
7744.2.a.bc 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(1\) \(3\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+2q^{7}-2q^{9}-4q^{13}+\cdots\)
7744.2.a.bd 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(2\) \(-1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-2q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
7744.2.a.be 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(2\) \(-1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-2q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
7744.2.a.bf 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(2\) \(-1\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+2q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
7744.2.a.bg 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(2\) \(-1\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
7744.2.a.bh 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(2\) \(3\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+3q^{5}-2q^{7}+q^{9}+5q^{13}+\cdots\)
7744.2.a.bi 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(2\) \(3\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+3q^{5}+2q^{7}+q^{9}-5q^{13}+\cdots\)
7744.2.a.bj 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(3\) \(-1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}+6q^{9}-6q^{13}-3q^{15}+\cdots\)
7744.2.a.bk 7744.a 1.a $1$ $61.836$ \(\Q\) None \(0\) \(3\) \(3\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+3q^{5}+2q^{7}+6q^{9}+9q^{15}+\cdots\)
7744.2.a.bl 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(-6\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-3q^{5}-2\beta q^{7}+q^{9}-3\beta q^{13}+\cdots\)
7744.2.a.bm 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-2+2\beta )q^{5}-2q^{7}+\cdots\)
7744.2.a.bn 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-2+2\beta )q^{5}+2q^{7}+\cdots\)
7744.2.a.bo 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(1\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+\beta q^{5}+(1-3\beta )q^{7}+\cdots\)
7744.2.a.bp 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(1\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+\beta q^{5}+(-1+3\beta )q^{7}+\cdots\)
7744.2.a.bq 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(-6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+\beta q^{5}+(-3-\beta )q^{7}+\cdots\)
7744.2.a.br 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-\beta q^{5}+(-1-\beta )q^{7}+\cdots\)
7744.2.a.bs 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-\beta q^{5}+(1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
7744.2.a.bt 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+\beta q^{5}+(3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7744.2.a.bu 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(4\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(2-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
7744.2.a.bv 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(4\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(2-\beta )q^{5}+(1-\beta )q^{7}+\cdots\)
7744.2.a.bw 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-3\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+2q^{13}+\cdots\)
7744.2.a.bx 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{33}) \) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(-3\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-\beta q^{3}+(-2+\beta )q^{5}+(5+\beta )q^{9}+(-8+\cdots)q^{15}+\cdots\)
7744.2.a.by 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-3\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots\)
7744.2.a.bz 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2\beta q^{5}+(2-4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
7744.2.a.ca 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2\beta q^{5}+(-2+4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
7744.2.a.cb 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(1\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}-\beta q^{7}+(-2+\beta )q^{9}+\cdots\)
7744.2.a.cc 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(1\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}+\beta q^{7}+(-2+\beta )q^{9}+\cdots\)
7744.2.a.cd 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}-2q^{7}+2q^{9}+2\beta q^{13}+\cdots\)
7744.2.a.ce 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(-1+\beta )q^{5}-3q^{9}+(-3+\beta )q^{13}+\cdots\)
7744.2.a.cf 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+(-1+\beta )q^{5}-3q^{9}+(3-\beta )q^{13}+\cdots\)
7744.2.a.cg 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+2q^{7}+2q^{9}-2\beta q^{13}+\cdots\)
7744.2.a.ch 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+(1-2\beta )q^{5}-3q^{9}+(-2-3\beta )q^{13}+\cdots\)
7744.2.a.ci 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+(1-2\beta )q^{5}-3q^{9}+(2+3\beta )q^{13}+\cdots\)
7744.2.a.cj 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(6\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+3q^{5}-2\beta q^{7}+2q^{9}-6q^{13}+\cdots\)
7744.2.a.ck 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(6\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+3q^{5}+2\beta q^{7}+2q^{9}+6q^{13}+\cdots\)
7744.2.a.cl 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-3\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2+\beta )q^{5}-2\beta q^{7}+(1+\beta )q^{9}+\cdots\)
7744.2.a.cm 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-3\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+2q^{13}+\cdots\)
7744.2.a.cn 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{33}) \) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(-3\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+\beta q^{3}+(-2+\beta )q^{5}+(5+\beta )q^{9}+(8+\cdots)q^{15}+\cdots\)
7744.2.a.co 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2\beta q^{5}+(-2+4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
7744.2.a.cp 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2\beta q^{5}+(2-4\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
7744.2.a.cq 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(1\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}-\beta q^{7}+(-2+\beta )q^{9}+\cdots\)
7744.2.a.cr 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(1\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}+\beta q^{7}+(-2+\beta )q^{9}+\cdots\)
7744.2.a.cs 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-\beta q^{5}+(-3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7744.2.a.ct 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-\beta q^{5}+(-1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
7744.2.a.cu 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-\beta q^{5}+(1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
7744.2.a.cv 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-\beta q^{5}+(3-\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
7744.2.a.cw 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(4\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
7744.2.a.cx 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(4\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
7744.2.a.cy 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-2+2\beta )q^{5}-2q^{7}+\cdots\)
7744.2.a.cz 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-2+2\beta )q^{5}+2q^{7}+\cdots\)
7744.2.a.da 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(1\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+\beta q^{5}+(1-3\beta )q^{7}+(-1+\cdots)q^{9}+\cdots\)
7744.2.a.db 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(1\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+\beta q^{5}+(-1+3\beta )q^{7}+\cdots\)
7744.2.a.dc 7744.a 1.a $2$ $61.836$ \(\Q(\sqrt{3}) \) None \(0\) \(4\) \(-6\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-3q^{5}-2\beta q^{7}+q^{9}+3\beta q^{13}+\cdots\)
7744.2.a.dd 7744.a 1.a $3$ $61.836$ 3.3.404.1 None \(0\) \(0\) \(3\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
7744.2.a.de 7744.a 1.a $3$ $61.836$ 3.3.404.1 None \(0\) \(0\) \(3\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
7744.2.a.df 7744.a 1.a $3$ $61.836$ 3.3.404.1 None \(0\) \(0\) \(3\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
7744.2.a.dg 7744.a 1.a $3$ $61.836$ 3.3.404.1 None \(0\) \(0\) \(3\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
7744.2.a.dh 7744.a 1.a $4$ $61.836$ 4.4.5225.1 None \(0\) \(-2\) \(-1\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
7744.2.a.di 7744.a 1.a $4$ $61.836$ 4.4.5225.1 None \(0\) \(-2\) \(-1\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
7744.2.a.dj 7744.a 1.a $4$ $61.836$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(-4\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-1+\beta _{3})q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
7744.2.a.dk 7744.a 1.a $4$ $61.836$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(-4\) \(8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-1-\beta _{3})q^{5}+(2+\beta _{3})q^{7}+\cdots\)
7744.2.a.dl 7744.a 1.a $4$ $61.836$ 4.4.22000.1 None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-2-3\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
7744.2.a.dm 7744.a 1.a $4$ $61.836$ 4.4.22000.1 None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-2-3\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
7744.2.a.dn 7744.a 1.a $4$ $61.836$ 4.4.7488.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+(5+2\beta _{1}+\cdots)q^{9}+\cdots\)
7744.2.a.do 7744.a 1.a $4$ $61.836$ 4.4.7488.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+(5+2\beta _{1}+\cdots)q^{9}+\cdots\)
7744.2.a.dp 7744.a 1.a $4$ $61.836$ 4.4.4400.1 None \(0\) \(0\) \(6\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+\beta _{1}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
7744.2.a.dq 7744.a 1.a $4$ $61.836$ 4.4.4400.1 None \(0\) \(0\) \(6\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}-\beta _{1}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
7744.2.a.dr 7744.a 1.a $4$ $61.836$ 4.4.5225.1 None \(0\) \(2\) \(-1\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
7744.2.a.ds 7744.a 1.a $4$ $61.836$ 4.4.5225.1 None \(0\) \(2\) \(-1\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
7744.2.a.dt 7744.a 1.a $6$ $61.836$ 6.6.19898000.1 None \(0\) \(-5\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{5}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
7744.2.a.du 7744.a 1.a $6$ $61.836$ 6.6.19898000.1 None \(0\) \(-5\) \(0\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{5}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
7744.2.a.dv 7744.a 1.a $6$ $61.836$ 6.6.19898000.1 None \(0\) \(5\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
7744.2.a.dw 7744.a 1.a $6$ $61.836$ 6.6.19898000.1 None \(0\) \(5\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7744))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7744)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1936))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3872))\)\(^{\oplus 2}\)