Properties

Label 7488.2.a
Level $7488$
Weight $2$
Character orbit 7488.a
Rep. character $\chi_{7488}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $82$
Sturm bound $2688$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 7488 = 2^{6} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7488.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 82 \)
Sturm bound: \(2688\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7488))\).

Total New Old
Modular forms 1392 120 1272
Cusp forms 1297 120 1177
Eisenstein series 95 0 95

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

\(2\)\(3\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(14\)
\(+\)\(-\)\(+\)\(-\)\(19\)
\(+\)\(-\)\(-\)\(+\)\(17\)
\(-\)\(+\)\(+\)\(-\)\(14\)
\(-\)\(+\)\(-\)\(+\)\(10\)
\(-\)\(-\)\(+\)\(+\)\(17\)
\(-\)\(-\)\(-\)\(-\)\(19\)
Plus space\(+\)\(54\)
Minus space\(-\)\(66\)

Trace form

\( 120 q + O(q^{10}) \) \( 120 q + 120 q^{25} - 16 q^{29} - 16 q^{37} + 16 q^{41} + 120 q^{49} - 64 q^{53} + 32 q^{61} + 32 q^{77} + 80 q^{85} + 32 q^{89} + 32 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7488))\) 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 3 13
7488.2.a.a 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-4\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-4q^{7}-4q^{11}+q^{13}+8q^{23}+\cdots\)
7488.2.a.b 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-4\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-4q^{7}-2q^{11}+q^{13}+6q^{17}+\cdots\)
7488.2.a.c 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-4\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}-2q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.d 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-4\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}+2q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.e 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-4\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+4q^{7}+2q^{11}+q^{13}+6q^{17}+\cdots\)
7488.2.a.f 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-4\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+4q^{7}+4q^{11}+q^{13}-8q^{23}+\cdots\)
7488.2.a.g 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-q^{7}+6q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.h 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}-6q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.i 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}-q^{13}-2q^{17}+8q^{19}+\cdots\)
7488.2.a.j 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}-4q^{11}+q^{13}+6q^{19}+\cdots\)
7488.2.a.k 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}+4q^{11}+q^{13}-2q^{19}+\cdots\)
7488.2.a.l 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}+6q^{11}+q^{13}+2q^{17}+\cdots\)
7488.2.a.m 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{11}-q^{13}+6q^{17}-8q^{19}+\cdots\)
7488.2.a.n 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{11}-q^{13}-4q^{19}+4q^{23}+\cdots\)
7488.2.a.o 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{11}-q^{13}+4q^{19}-4q^{23}+\cdots\)
7488.2.a.p 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{11}-q^{13}+6q^{17}+8q^{19}+\cdots\)
7488.2.a.q 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}-6q^{11}+q^{13}+2q^{17}+\cdots\)
7488.2.a.r 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}-4q^{11}+q^{13}+2q^{19}+\cdots\)
7488.2.a.s 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}+4q^{11}+q^{13}-6q^{19}+\cdots\)
7488.2.a.t 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{7}-q^{13}-2q^{17}-8q^{19}+\cdots\)
7488.2.a.u 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-1\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-5q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.v 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.w 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.x 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(-1\) \(5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+5q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.y 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-2q^{11}+q^{13}+6q^{17}+4q^{19}+\cdots\)
7488.2.a.z 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-4q^{11}-q^{13}+6q^{17}+6q^{19}+\cdots\)
7488.2.a.ba 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-q^{13}-2q^{17}-2q^{19}+8q^{23}+\cdots\)
7488.2.a.bb 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
7488.2.a.bc 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-6q^{11}+q^{13}-2q^{17}+4q^{23}-5q^{25}+\cdots\)
7488.2.a.bd 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+6q^{11}+q^{13}-2q^{17}-4q^{23}-5q^{25}+\cdots\)
7488.2.a.be 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-q^{13}-2q^{17}+2q^{19}-8q^{23}+\cdots\)
7488.2.a.bf 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-q^{13}+6q^{17}-2q^{19}-5q^{25}+\cdots\)
7488.2.a.bg 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}+4q^{11}-q^{13}+6q^{17}-6q^{19}+\cdots\)
7488.2.a.bh 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}+2q^{11}+q^{13}+6q^{17}-4q^{19}+\cdots\)
7488.2.a.bi 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(1\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{7}-2q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.bj 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(1\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}+2q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.bk 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.bl 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.bm 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-4q^{11}+q^{13}-2q^{19}+\cdots\)
7488.2.a.bn 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bo 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}+2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bp 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}+4q^{11}+q^{13}+6q^{19}+\cdots\)
7488.2.a.bq 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{11}-q^{13}+4q^{19}+4q^{23}+\cdots\)
7488.2.a.br 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{13}-2q^{17}-4q^{19}-q^{25}+\cdots\)
7488.2.a.bs 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{13}-2q^{17}+4q^{19}-q^{25}+\cdots\)
7488.2.a.bt 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{11}-q^{13}-4q^{19}-4q^{23}+\cdots\)
7488.2.a.bu 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}-4q^{11}+q^{13}-6q^{19}+\cdots\)
7488.2.a.bv 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}-2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bw 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bx 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+4q^{11}+q^{13}+2q^{19}+\cdots\)
7488.2.a.by 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.bz 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.ca 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(4\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-4q^{7}+4q^{11}+q^{13}-8q^{23}+\cdots\)
7488.2.a.cb 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-2q^{11}+q^{13}-2q^{17}-8q^{19}+\cdots\)
7488.2.a.cc 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+2q^{11}+q^{13}-2q^{17}+8q^{19}+\cdots\)
7488.2.a.cd 7488.a 1.a $1$ $59.792$ \(\Q\) None \(0\) \(0\) \(4\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+4q^{7}-4q^{11}+q^{13}+8q^{23}+\cdots\)
7488.2.a.ce 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(-1-\beta )q^{7}-2q^{11}+\cdots\)
7488.2.a.cf 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(1+\beta )q^{7}+2q^{11}+\cdots\)
7488.2.a.cg 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(-3+\beta )q^{7}+2\beta q^{11}+\cdots\)
7488.2.a.ch 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(3-\beta )q^{7}-2\beta q^{11}+\cdots\)
7488.2.a.ci 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-2-\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
7488.2.a.cj 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-\beta q^{11}-q^{13}-2\beta q^{17}+2q^{19}+\cdots\)
7488.2.a.ck 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-2+\beta )q^{7}+(2-\beta )q^{11}+\cdots\)
7488.2.a.cl 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-\beta q^{7}-2q^{11}+q^{13}+(-2+\cdots)q^{17}+\cdots\)
7488.2.a.cm 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{7}+\beta q^{11}+q^{13}+\beta q^{19}-2\beta q^{23}+\cdots\)
7488.2.a.cn 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{7}+\beta q^{11}+q^{13}-\beta q^{19}-2\beta q^{23}+\cdots\)
7488.2.a.co 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+\beta q^{7}+2q^{11}+q^{13}+(-2+\cdots)q^{17}+\cdots\)
7488.2.a.cp 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(2-\beta )q^{7}+(-2+\beta )q^{11}+\cdots\)
7488.2.a.cq 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-\beta q^{11}-q^{13}+2\beta q^{17}-2q^{19}+\cdots\)
7488.2.a.cr 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(2+\beta )q^{7}+(2+\beta )q^{11}-q^{13}+\cdots\)
7488.2.a.cs 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1-\beta )q^{7}-2q^{11}+\cdots\)
7488.2.a.ct 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(1+\beta )q^{7}+2q^{11}+q^{13}+\cdots\)
7488.2.a.cu 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(-2+2\beta )q^{11}+\cdots\)
7488.2.a.cv 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(1-\beta )q^{7}+(2-2\beta )q^{11}+\cdots\)
7488.2.a.cw 7488.a 1.a $2$ $59.792$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+\beta q^{7}-2\beta q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.cx 7488.a 1.a $3$ $59.792$ 3.3.148.1 None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{5}+\beta _{2}q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
7488.2.a.cy 7488.a 1.a $3$ $59.792$ 3.3.148.1 None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{5}-\beta _{2}q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
7488.2.a.cz 7488.a 1.a $4$ $59.792$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
7488.2.a.da 7488.a 1.a $4$ $59.792$ 4.4.13448.1 None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\beta _{1}q^{11}+\cdots\)
7488.2.a.db 7488.a 1.a $4$ $59.792$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+\beta _{3}q^{7}+(-2-\beta _{2})q^{11}+\cdots\)
7488.2.a.dc 7488.a 1.a $4$ $59.792$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(2+\beta _{2})q^{11}+q^{13}+\cdots\)
7488.2.a.dd 7488.a 1.a $4$ $59.792$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7488))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7488)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(936))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1872))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2496))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3744))\)\(^{\oplus 2}\)