Properties

Label 8464.2.a
Level $8464$
Weight $2$
Character orbit 8464.a
Rep. character $\chi_{8464}(1,\cdot)$
Character field $\Q$
Dimension $242$
Newform subspaces $62$
Sturm bound $2208$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 8464 = 2^{4} \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8464.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 62 \)
Sturm bound: \(2208\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8464))\).

Total New Old
Modular forms 1176 263 913
Cusp forms 1033 242 791
Eisenstein series 143 21 122

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

\(2\)\(23\)FrickeDim
\(+\)\(+\)$+$\(60\)
\(+\)\(-\)$-$\(66\)
\(-\)\(+\)$-$\(61\)
\(-\)\(-\)$+$\(55\)
Plus space\(+\)\(115\)
Minus space\(-\)\(127\)

Trace form

\( 242 q - 2 q^{3} + 2 q^{5} - 4 q^{7} + 224 q^{9} + O(q^{10}) \) \( 242 q - 2 q^{3} + 2 q^{5} - 4 q^{7} + 224 q^{9} + 2 q^{13} + 2 q^{17} - 4 q^{19} + 204 q^{25} - 8 q^{27} + 2 q^{29} - 10 q^{31} + 8 q^{33} + 10 q^{37} - 20 q^{39} - 6 q^{41} + 10 q^{45} + 44 q^{47} + 176 q^{49} - 4 q^{51} + 10 q^{53} + 24 q^{55} - 8 q^{57} - 2 q^{59} + 18 q^{61} - 32 q^{63} - 12 q^{65} + 8 q^{67} + 6 q^{71} + 2 q^{73} - 6 q^{75} + 8 q^{77} - 28 q^{79} + 162 q^{81} + 20 q^{83} + 12 q^{85} + 40 q^{87} - 6 q^{89} - 4 q^{91} - 22 q^{93} - 8 q^{95} - 6 q^{97} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8464))\) 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 23
8464.2.a.a 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(-3\) \(-2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{5}-2q^{7}+6q^{9}+4q^{11}+\cdots\)
8464.2.a.b 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(-3\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+6q^{9}-5q^{13}+6q^{17}+\cdots\)
8464.2.a.c 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(-3\) \(2\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+2q^{5}+2q^{7}+6q^{9}-4q^{11}+\cdots\)
8464.2.a.d 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
8464.2.a.e 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(-2\) \(1\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
8464.2.a.f 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}-2q^{9}-q^{13}+6q^{17}+\cdots\)
8464.2.a.g 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(0\) \(-4\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-4q^{7}-3q^{9}+2q^{11}-2q^{13}+\cdots\)
8464.2.a.h 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}-4q^{11}+q^{13}+\cdots\)
8464.2.a.i 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{9}+6q^{11}-2q^{13}-6q^{17}+\cdots\)
8464.2.a.j 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{9}+4q^{11}+q^{13}+\cdots\)
8464.2.a.k 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(1\) \(-2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
8464.2.a.l 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(1\) \(-2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+2q^{7}-2q^{9}-6q^{11}+\cdots\)
8464.2.a.m 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(1\) \(2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-4q^{7}-2q^{9}-2q^{11}+\cdots\)
8464.2.a.n 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(1\) \(2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-2q^{7}-2q^{9}+6q^{11}+\cdots\)
8464.2.a.o 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(1\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots\)
8464.2.a.p 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(1\) \(4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}+2q^{7}-2q^{9}-4q^{11}+\cdots\)
8464.2.a.q 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(2\) \(-3\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-3q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
8464.2.a.r 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(2\) \(3\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+3q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
8464.2.a.s 8464.a 1.a $1$ $67.585$ \(\Q\) None \(0\) \(3\) \(2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{5}-4q^{7}+6q^{9}+2q^{11}+\cdots\)
8464.2.a.t 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2\beta q^{7}+q^{9}+3\beta q^{11}+6q^{13}+\cdots\)
8464.2.a.u 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+\beta q^{5}+(-3-\beta )q^{7}+\cdots\)
8464.2.a.v 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+\beta q^{7}-2q^{9}+\beta q^{11}+\cdots\)
8464.2.a.w 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2\beta q^{5}-2\beta q^{7}-2q^{9}+2\beta q^{11}+\cdots\)
8464.2.a.x 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-\beta q^{5}+(3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
8464.2.a.y 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-6\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-3q^{5}+(-2-\beta )q^{7}+3q^{9}+\cdots\)
8464.2.a.z 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-2\beta )q^{5}+(2-\beta )q^{7}+\cdots\)
8464.2.a.ba 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1+2\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
8464.2.a.bb 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+2q^{9}+\cdots\)
8464.2.a.bc 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(6\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+3q^{5}+(2+\beta )q^{7}+3q^{9}+\beta q^{11}+\cdots\)
8464.2.a.bd 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-4\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)
8464.2.a.be 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-4\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-2-\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
8464.2.a.bf 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
8464.2.a.bg 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(-2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}-q^{5}-3\beta q^{7}+(3+4\beta )q^{9}+\cdots\)
8464.2.a.bh 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{3}) \) None \(0\) \(4\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-2\beta q^{11}+\cdots\)
8464.2.a.bi 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{3}) \) None \(0\) \(4\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+q^{13}+\cdots\)
8464.2.a.bj 8464.a 1.a $2$ $67.585$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+q^{5}+3\beta q^{7}+(3+4\beta )q^{9}+\cdots\)
8464.2.a.bk 8464.a 1.a $3$ $67.585$ 3.3.621.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+\beta _{2}q^{3}+(3-\beta _{1}-\beta _{2})q^{9}+(\beta _{1}-\beta _{2})q^{13}+\cdots\)
8464.2.a.bl 8464.a 1.a $4$ $67.585$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(-8\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{3})q^{3}+(-2-\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
8464.2.a.bm 8464.a 1.a $4$ $67.585$ \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+2q^{9}+\cdots\)
8464.2.a.bn 8464.a 1.a $4$ $67.585$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(8\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{3})q^{3}+(2+\beta _{1})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
8464.2.a.bo 8464.a 1.a $4$ $67.585$ 4.4.9248.1 None \(0\) \(2\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-\beta _{1}q^{5}-\beta _{3}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
8464.2.a.bp 8464.a 1.a $4$ $67.585$ \(\Q(\sqrt{2}, \sqrt{13})\) None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}-2q^{9}+\cdots\)
8464.2.a.bq 8464.a 1.a $4$ $67.585$ \(\Q(\zeta_{24})^+\) None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}+(\beta _{1}+2\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8464.2.a.br 8464.a 1.a $4$ $67.585$ \(\Q(\zeta_{24})^+\) None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
8464.2.a.bs 8464.a 1.a $5$ $67.585$ \(\Q(\zeta_{22})^+\) None \(0\) \(-2\) \(-7\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
8464.2.a.bt 8464.a 1.a $5$ $67.585$ \(\Q(\zeta_{22})^+\) None \(0\) \(-2\) \(7\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{4})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
8464.2.a.bu 8464.a 1.a $5$ $67.585$ \(\Q(\zeta_{22})^+\) None \(0\) \(0\) \(-2\) \(9\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1}+\beta _{3}-\beta _{4})q^{5}+\cdots\)
8464.2.a.bv 8464.a 1.a $5$ $67.585$ \(\Q(\zeta_{22})^+\) None \(0\) \(0\) \(2\) \(-9\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{5}+\cdots\)
8464.2.a.bw 8464.a 1.a $5$ $67.585$ \(\Q(\zeta_{22})^+\) None \(0\) \(2\) \(-8\) \(7\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{4})q^{3}+(-2+\beta _{1}+\beta _{3})q^{5}+\cdots\)
8464.2.a.bx 8464.a 1.a $5$ $67.585$ \(\Q(\zeta_{22})^+\) None \(0\) \(2\) \(8\) \(-7\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{4})q^{3}+(2-\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
8464.2.a.by 8464.a 1.a $6$ $67.585$ 6.6.26849792.2 None \(0\) \(-4\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(-\beta _{3}+\beta _{4})q^{5}-\beta _{2}q^{7}+\cdots\)
8464.2.a.bz 8464.a 1.a $6$ $67.585$ 6.6.197448192.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{5}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(3+\cdots)q^{9}+\cdots\)
8464.2.a.ca 8464.a 1.a $8$ $67.585$ 8.8.5780865024.1 None \(0\) \(-4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{5})q^{3}-\beta _{7}q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
8464.2.a.cb 8464.a 1.a $8$ $67.585$ 8.8.\(\cdots\).1 None \(0\) \(-4\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{4})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
8464.2.a.cc 8464.a 1.a $8$ $67.585$ 8.8.\(\cdots\).1 None \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{6}q^{3}+\beta _{1}q^{5}+(\beta _{3}+\beta _{5})q^{7}+(2+\cdots)q^{9}+\cdots\)
8464.2.a.cd 8464.a 1.a $10$ $67.585$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-1\) \(-12\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{4})q^{3}+(-1-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{5}+\cdots\)
8464.2.a.ce 8464.a 1.a $10$ $67.585$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-1\) \(12\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{4})q^{3}+(1+\beta _{2}-\beta _{3}-\beta _{6}+\cdots)q^{5}+\cdots\)
8464.2.a.cf 8464.a 1.a $12$ $67.585$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-8\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{9}q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
8464.2.a.cg 8464.a 1.a $15$ $67.585$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(-1\) \(0\) \(-10\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{5}+\beta _{10})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
8464.2.a.ch 8464.a 1.a $15$ $67.585$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(-1\) \(0\) \(10\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{5}-\beta _{10})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8464.2.a.ci 8464.a 1.a $15$ $67.585$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(1\) \(-10\) \(10\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1-\beta _{13})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
8464.2.a.cj 8464.a 1.a $15$ $67.585$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(1\) \(10\) \(-10\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{13})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8464))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8464)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4232))\)\(^{\oplus 2}\)