Properties

Label 8112.2.a
Level $8112$
Weight $2$
Character orbit 8112.a
Rep. character $\chi_{8112}(1,\cdot)$
Character field $\Q$
Dimension $155$
Newform subspaces $75$
Sturm bound $2912$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8112.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 75 \)
Sturm bound: \(2912\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8112))\).

Total New Old
Modular forms 1540 155 1385
Cusp forms 1373 155 1218
Eisenstein series 167 0 167

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.
\(+\)\(+\)\(+\)\(+\)\(18\)
\(+\)\(+\)\(-\)\(-\)\(21\)
\(+\)\(-\)\(+\)\(-\)\(23\)
\(+\)\(-\)\(-\)\(+\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(-\)\(+\)\(21\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(21\)
Plus space\(+\)\(72\)
Minus space\(-\)\(83\)

Trace form

\( 155 q - q^{3} + 2 q^{5} - 4 q^{7} + 155 q^{9} + O(q^{10}) \) \( 155 q - q^{3} + 2 q^{5} - 4 q^{7} + 155 q^{9} - 4 q^{11} - 2 q^{15} - 2 q^{17} + 8 q^{23} + 149 q^{25} - q^{27} + 10 q^{29} - 12 q^{31} - 4 q^{33} + 10 q^{37} + 6 q^{41} - 4 q^{43} + 2 q^{45} - 24 q^{47} + 155 q^{49} - 10 q^{51} + 18 q^{53} + 16 q^{55} - 4 q^{57} + 4 q^{59} + 18 q^{61} - 4 q^{63} - 24 q^{67} + 8 q^{69} + 24 q^{71} - 18 q^{73} + q^{75} + 16 q^{77} - 24 q^{79} + 155 q^{81} + 44 q^{83} + 4 q^{85} - 6 q^{87} + 6 q^{89} - 8 q^{93} - 16 q^{95} + 6 q^{97} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8112))\) 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
8112.2.a.a 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(-4\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
8112.2.a.b 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(-3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+q^{9}+3q^{15}-q^{17}+\cdots\)
8112.2.a.c 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(-3\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
8112.2.a.d 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots\)
8112.2.a.e 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.f 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}+2q^{15}+2q^{17}+\cdots\)
8112.2.a.g 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(-2\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{15}+\cdots\)
8112.2.a.h 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+6q^{11}+2q^{17}-4q^{23}+\cdots\)
8112.2.a.i 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-6q^{17}+2q^{19}+\cdots\)
8112.2.a.j 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-2q^{7}+q^{9}-2q^{15}+\cdots\)
8112.2.a.k 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
8112.2.a.l 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(2\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots\)
8112.2.a.m 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(3\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
8112.2.a.n 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}+q^{9}-3q^{15}-q^{17}+\cdots\)
8112.2.a.o 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(4\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)
8112.2.a.p 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(-1\) \(4\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
8112.2.a.q 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+q^{9}-2q^{11}-4q^{15}+\cdots\)
8112.2.a.r 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(-3\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
8112.2.a.s 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(-2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
8112.2.a.t 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}+6q^{11}-2q^{15}+\cdots\)
8112.2.a.u 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(-2\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}-2q^{15}+\cdots\)
8112.2.a.v 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(-2\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.w 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}-q^{15}+\cdots\)
8112.2.a.x 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-q^{15}+\cdots\)
8112.2.a.y 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}-2q^{11}-6q^{17}+\cdots\)
8112.2.a.z 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{17}+\cdots\)
8112.2.a.ba 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{17}+\cdots\)
8112.2.a.bb 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}+q^{15}+\cdots\)
8112.2.a.bc 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+q^{15}+\cdots\)
8112.2.a.bd 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-q^{7}+q^{9}-2q^{11}+2q^{15}+\cdots\)
8112.2.a.be 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{15}+\cdots\)
8112.2.a.bf 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(2\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{15}+\cdots\)
8112.2.a.bg 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{15}+\cdots\)
8112.2.a.bh 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(3\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.bi 8112.a 1.a $1$ $64.775$ \(\Q\) None \(0\) \(1\) \(4\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.bj 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-4\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2+\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
8112.2.a.bk 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-3\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
8112.2.a.bl 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-1+\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
8112.2.a.bm 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-2q^{11}+\cdots\)
8112.2.a.bn 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(2\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8112.2.a.bo 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(3\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots\)
8112.2.a.bp 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(4\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(2+\beta )q^{5}+(1+\beta )q^{7}+q^{9}+\cdots\)
8112.2.a.bq 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+(-3+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
8112.2.a.br 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8112.2.a.bs 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots\)
8112.2.a.bt 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-2\beta q^{11}+\cdots\)
8112.2.a.bu 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2\beta q^{5}-\beta q^{7}+q^{9}+2\beta q^{11}+\cdots\)
8112.2.a.bv 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{7}+q^{9}-\beta q^{11}+6q^{17}+\cdots\)
8112.2.a.bw 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+(1-\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
8112.2.a.bx 8112.a 1.a $2$ $64.775$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+(3+\beta )q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
8112.2.a.by 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(-4\) \(10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta _{1})q^{5}+(3+\beta _{1})q^{7}+\cdots\)
8112.2.a.bz 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(-3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ca 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(0\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cb 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
8112.2.a.cc 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cd 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(0\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(3-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ce 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(3\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\cdots\)
8112.2.a.cf 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(4\) \(-10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta _{1})q^{5}+(-3-\beta _{1})q^{7}+\cdots\)
8112.2.a.cg 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(-6\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-2+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
8112.2.a.ch 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(-2\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ci 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta _{2})q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
8112.2.a.cj 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(-1\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-3\beta _{1}+\beta _{2})q^{5}+(4-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ck 8112.a 1.a $3$ $64.775$ 3.3.837.1 None \(0\) \(3\) \(0\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+q^{9}+\cdots\)
8112.2.a.cl 8112.a 1.a $3$ $64.775$ 3.3.837.1 None \(0\) \(3\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{2}q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
8112.2.a.cm 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(1\) \(-9\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-2-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cn 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
8112.2.a.co 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(2\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
8112.2.a.cp 8112.a 1.a $3$ $64.775$ \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(6\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(2-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
8112.2.a.cq 8112.a 1.a $4$ $64.775$ 4.4.25488.1 None \(0\) \(-4\) \(-4\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cr 8112.a 1.a $4$ $64.775$ \(\Q(\sqrt{3}, \sqrt{43})\) None \(0\) \(-4\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
8112.2.a.cs 8112.a 1.a $4$ $64.775$ 4.4.25488.1 None \(0\) \(-4\) \(4\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ct 8112.a 1.a $6$ $64.775$ 6.6.27700337.1 None \(0\) \(-6\) \(-1\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
8112.2.a.cu 8112.a 1.a $6$ $64.775$ 6.6.27700337.1 None \(0\) \(-6\) \(1\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
8112.2.a.cv 8112.a 1.a $6$ $64.775$ 6.6.27700337.1 None \(0\) \(6\) \(-1\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{5}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
8112.2.a.cw 8112.a 1.a $6$ $64.775$ 6.6.27700337.1 None \(0\) \(6\) \(1\) \(-7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{5}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8112))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8112)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2028))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4056))\)\(^{\oplus 2}\)