Properties

Label 7938.2.a
Level $7938$
Weight $2$
Character orbit 7938.a
Rep. character $\chi_{7938}(1,\cdot)$
Character field $\Q$
Dimension $164$
Newform subspaces $74$
Sturm bound $3024$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7938.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 74 \)
Sturm bound: \(3024\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7938))\).

Total New Old
Modular forms 1608 164 1444
Cusp forms 1417 164 1253
Eisenstein series 191 0 191

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

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(20\)
\(+\)\(+\)\(-\)\(-\)\(21\)
\(+\)\(-\)\(+\)\(-\)\(20\)
\(+\)\(-\)\(-\)\(+\)\(21\)
\(-\)\(+\)\(+\)\(-\)\(24\)
\(-\)\(+\)\(-\)\(+\)\(18\)
\(-\)\(-\)\(+\)\(+\)\(16\)
\(-\)\(-\)\(-\)\(-\)\(24\)
Plus space\(+\)\(75\)
Minus space\(-\)\(89\)

Trace form

\( 164 q + 164 q^{4} + O(q^{10}) \) \( 164 q + 164 q^{4} + 6 q^{10} + 10 q^{13} + 164 q^{16} - 2 q^{19} - 6 q^{22} + 158 q^{25} - 8 q^{31} - 2 q^{37} + 6 q^{40} - 26 q^{43} + 12 q^{46} + 10 q^{52} - 24 q^{55} + 18 q^{58} - 2 q^{61} + 164 q^{64} - 38 q^{67} - 44 q^{73} - 2 q^{76} + 40 q^{79} + 6 q^{82} + 18 q^{85} - 6 q^{88} - 12 q^{94} + 22 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7938))\) 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 7
7938.2.a.a 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}-2q^{11}+\cdots\)
7938.2.a.b 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}-3q^{11}+\cdots\)
7938.2.a.c 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+3q^{11}+\cdots\)
7938.2.a.d 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+6q^{11}+\cdots\)
7938.2.a.e 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots\)
7938.2.a.f 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots\)
7938.2.a.g 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}-4q^{13}+q^{16}-6q^{17}+\cdots\)
7938.2.a.h 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+4q^{13}+q^{16}+6q^{17}+\cdots\)
7938.2.a.i 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+3q^{11}-2q^{13}+\cdots\)
7938.2.a.j 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
7938.2.a.k 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+2q^{11}+\cdots\)
7938.2.a.l 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}-6q^{11}+\cdots\)
7938.2.a.m 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}-3q^{11}+\cdots\)
7938.2.a.n 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+q^{13}+\cdots\)
7938.2.a.o 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots\)
7938.2.a.p 7938.a 1.a $1$ $63.385$ \(\Q\) None \(-1\) \(0\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{5}-q^{8}-4q^{10}-2q^{11}+\cdots\)
7938.2.a.q 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+2q^{11}+\cdots\)
7938.2.a.r 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
7938.2.a.s 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{13}+\cdots\)
7938.2.a.t 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+3q^{11}+\cdots\)
7938.2.a.u 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+6q^{11}+\cdots\)
7938.2.a.v 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-2q^{11}+\cdots\)
7938.2.a.w 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+2q^{11}+\cdots\)
7938.2.a.x 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-3q^{11}-2q^{13}+\cdots\)
7938.2.a.y 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-4q^{13}+q^{16}+6q^{17}+\cdots\)
7938.2.a.z 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+4q^{13}+q^{16}-6q^{17}+\cdots\)
7938.2.a.ba 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-2q^{11}+\cdots\)
7938.2.a.bb 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots\)
7938.2.a.bc 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-6q^{11}+\cdots\)
7938.2.a.bd 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
7938.2.a.be 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+3q^{11}+\cdots\)
7938.2.a.bf 7938.a 1.a $1$ $63.385$ \(\Q\) None \(1\) \(0\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+2q^{11}+\cdots\)
7938.2.a.bg 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-2+\beta )q^{5}-q^{8}+(2+\cdots)q^{10}+\cdots\)
7938.2.a.bh 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{33}) \) None \(-2\) \(0\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta )q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
7938.2.a.bi 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+(-3+\cdots)q^{11}+\cdots\)
7938.2.a.bj 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}-\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
7938.2.a.bk 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+\beta q^{11}+(2-\beta )q^{13}+\cdots\)
7938.2.a.bl 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+2q^{11}+\cdots\)
7938.2.a.bm 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
7938.2.a.bn 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
7938.2.a.bo 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-2q^{11}+\cdots\)
7938.2.a.bp 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
7938.2.a.bq 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+\beta q^{11}+(2+\beta )q^{13}+\cdots\)
7938.2.a.br 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+(3+\cdots)q^{11}+\cdots\)
7938.2.a.bs 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{8}+(1+\beta )q^{10}+\cdots\)
7938.2.a.bt 7938.a 1.a $2$ $63.385$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(2+\beta )q^{5}+q^{8}+(2+\beta )q^{10}+\cdots\)
7938.2.a.bu 7938.a 1.a $3$ $63.385$ 3.3.321.1 None \(-3\) \(0\) \(-5\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-2+\beta _{1})q^{5}-q^{8}+(2+\cdots)q^{10}+\cdots\)
7938.2.a.bv 7938.a 1.a $3$ $63.385$ 3.3.321.1 None \(-3\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{2}q^{5}-q^{8}-\beta _{2}q^{10}+\cdots\)
7938.2.a.bw 7938.a 1.a $3$ $63.385$ 3.3.321.1 None \(-3\) \(0\) \(1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{2}q^{5}-q^{8}+\beta _{2}q^{10}+\cdots\)
7938.2.a.bx 7938.a 1.a $3$ $63.385$ 3.3.321.1 None \(-3\) \(0\) \(5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(2-\beta _{1})q^{5}-q^{8}+(-2+\cdots)q^{10}+\cdots\)
7938.2.a.by 7938.a 1.a $3$ $63.385$ 3.3.321.1 None \(3\) \(0\) \(-5\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-2+\beta _{1})q^{5}+q^{8}+(-2+\cdots)q^{10}+\cdots\)
7938.2.a.bz 7938.a 1.a $3$ $63.385$ 3.3.321.1 None \(3\) \(0\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots\)
7938.2.a.ca 7938.a 1.a $3$ $63.385$ 3.3.321.1 None \(3\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta _{2}q^{5}+q^{8}-\beta _{2}q^{10}+\cdots\)
7938.2.a.cb 7938.a 1.a $3$ $63.385$ 3.3.321.1 None \(3\) \(0\) \(5\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(2-\beta _{1})q^{5}+q^{8}+(2-\beta _{1}+\cdots)q^{10}+\cdots\)
7938.2.a.cc 7938.a 1.a $4$ $63.385$ 4.4.21312.1 None \(-4\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta _{3})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
7938.2.a.cd 7938.a 1.a $4$ $63.385$ \(\Q(\sqrt{2}, \sqrt{15})\) None \(-4\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
7938.2.a.ce 7938.a 1.a $4$ $63.385$ \(\Q(\sqrt{2}, \sqrt{15})\) None \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
7938.2.a.cf 7938.a 1.a $4$ $63.385$ 4.4.21312.1 None \(-4\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{3}q^{5}-q^{8}-\beta _{3}q^{10}+\cdots\)
7938.2.a.cg 7938.a 1.a $4$ $63.385$ \(\Q(\sqrt{2}, \sqrt{15})\) None \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
7938.2.a.ch 7938.a 1.a $4$ $63.385$ \(\Q(\sqrt{7}, \sqrt{15})\) None \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{3}q^{5}-q^{8}-\beta _{3}q^{10}+\cdots\)
7938.2.a.ci 7938.a 1.a $4$ $63.385$ \(\Q(\zeta_{24})^+\) None \(-4\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2\beta _{1}q^{5}-q^{8}-2\beta _{1}q^{10}+\cdots\)
7938.2.a.cj 7938.a 1.a $4$ $63.385$ \(\Q(\zeta_{24})^+\) None \(-4\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
7938.2.a.ck 7938.a 1.a $4$ $63.385$ \(\Q(\zeta_{24})^+\) None \(-4\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
7938.2.a.cl 7938.a 1.a $4$ $63.385$ 4.4.21312.1 None \(-4\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta _{3})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
7938.2.a.cm 7938.a 1.a $4$ $63.385$ 4.4.21312.1 None \(4\) \(0\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta _{3})q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
7938.2.a.cn 7938.a 1.a $4$ $63.385$ \(\Q(\zeta_{24})^+\) None \(4\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots\)
7938.2.a.co 7938.a 1.a $4$ $63.385$ \(\Q(\zeta_{24})^+\) None \(4\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots\)
7938.2.a.cp 7938.a 1.a $4$ $63.385$ \(\Q(\zeta_{24})^+\) None \(4\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2\beta _{1}q^{5}+q^{8}+2\beta _{1}q^{10}+\cdots\)
7938.2.a.cq 7938.a 1.a $4$ $63.385$ \(\Q(\sqrt{7}, \sqrt{15})\) None \(4\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{3}q^{5}+q^{8}+\beta _{3}q^{10}+\cdots\)
7938.2.a.cr 7938.a 1.a $4$ $63.385$ \(\Q(\sqrt{2}, \sqrt{15})\) None \(4\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots\)
7938.2.a.cs 7938.a 1.a $4$ $63.385$ 4.4.21312.1 None \(4\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{3}q^{5}+q^{8}+\beta _{3}q^{10}+\cdots\)
7938.2.a.ct 7938.a 1.a $4$ $63.385$ \(\Q(\sqrt{2}, \sqrt{15})\) None \(4\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots\)
7938.2.a.cu 7938.a 1.a $4$ $63.385$ \(\Q(\sqrt{2}, \sqrt{15})\) None \(4\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{1}q^{5}+q^{8}+\beta _{1}q^{10}+\cdots\)
7938.2.a.cv 7938.a 1.a $4$ $63.385$ 4.4.21312.1 None \(4\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta _{3})q^{5}+q^{8}+(1+\beta _{3})q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7938))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7938)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(567))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1134))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1323))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2646))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3969))\)\(^{\oplus 2}\)