Properties

Label 2496.4.a
Level $2496$
Weight $4$
Character orbit 2496.a
Rep. character $\chi_{2496}(1,\cdot)$
Character field $\Q$
Dimension $144$
Newform subspaces $58$
Sturm bound $1792$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2496.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 58 \)
Sturm bound: \(1792\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2496))\).

Total New Old
Modular forms 1368 144 1224
Cusp forms 1320 144 1176
Eisenstein series 48 0 48

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
\(+\)\(+\)\(+\)\(+\)\(18\)
\(+\)\(+\)\(-\)\(-\)\(18\)
\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(-\)\(-\)\(+\)\(20\)
\(-\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(-\)\(+\)\(18\)
\(-\)\(-\)\(+\)\(+\)\(20\)
\(-\)\(-\)\(-\)\(-\)\(16\)
Plus space\(+\)\(76\)
Minus space\(-\)\(68\)

Trace form

\( 144 q + 1296 q^{9} + O(q^{10}) \) \( 144 q + 1296 q^{9} + 3600 q^{25} - 800 q^{29} - 32 q^{37} + 7056 q^{49} + 1504 q^{53} - 1824 q^{61} - 1056 q^{69} + 10816 q^{77} + 11664 q^{81} + 5184 q^{85} - 2976 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2496))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 13
2496.4.a.a 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.c \(0\) \(-3\) \(-10\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-10q^{5}-8q^{7}+9q^{9}-40q^{11}+\cdots\)
2496.4.a.b 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.e \(0\) \(-3\) \(-6\) \(-20\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-6q^{5}-20q^{7}+9q^{9}+24q^{11}+\cdots\)
2496.4.a.c 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.f \(0\) \(-3\) \(-4\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-4q^{5}+4q^{7}+9q^{9}-2q^{11}+\cdots\)
2496.4.a.d 2496.a 1.a $1$ $147.269$ \(\Q\) None 156.4.a.b \(0\) \(-3\) \(2\) \(-32\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+2q^{5}-2^{5}q^{7}+9q^{9}+68q^{11}+\cdots\)
2496.4.a.e 2496.a 1.a $1$ $147.269$ \(\Q\) None 156.4.a.a \(0\) \(-3\) \(6\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+6q^{5}+4q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
2496.4.a.f 2496.a 1.a $1$ $147.269$ \(\Q\) None 39.4.a.a \(0\) \(-3\) \(12\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+12q^{5}-2q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
2496.4.a.g 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.a \(0\) \(-3\) \(16\) \(-28\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+2^{4}q^{5}-28q^{7}+9q^{9}+34q^{11}+\cdots\)
2496.4.a.h 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.b \(0\) \(-3\) \(16\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+2^{4}q^{5}-8q^{7}+9q^{9}+38q^{11}+\cdots\)
2496.4.a.i 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.d \(0\) \(-3\) \(20\) \(32\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+20q^{5}+2^{5}q^{7}+9q^{9}+50q^{11}+\cdots\)
2496.4.a.j 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.c \(0\) \(3\) \(-10\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-10q^{5}+8q^{7}+9q^{9}+40q^{11}+\cdots\)
2496.4.a.k 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.e \(0\) \(3\) \(-6\) \(20\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-6q^{5}+20q^{7}+9q^{9}-24q^{11}+\cdots\)
2496.4.a.l 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.f \(0\) \(3\) \(-4\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-4q^{5}-4q^{7}+9q^{9}+2q^{11}+\cdots\)
2496.4.a.m 2496.a 1.a $1$ $147.269$ \(\Q\) None 156.4.a.b \(0\) \(3\) \(2\) \(32\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{5}+2^{5}q^{7}+9q^{9}-68q^{11}+\cdots\)
2496.4.a.n 2496.a 1.a $1$ $147.269$ \(\Q\) None 156.4.a.a \(0\) \(3\) \(6\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+6q^{5}-4q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
2496.4.a.o 2496.a 1.a $1$ $147.269$ \(\Q\) None 39.4.a.a \(0\) \(3\) \(12\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+12q^{5}+2q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
2496.4.a.p 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.b \(0\) \(3\) \(16\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2^{4}q^{5}+8q^{7}+9q^{9}-38q^{11}+\cdots\)
2496.4.a.q 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.a \(0\) \(3\) \(16\) \(28\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2^{4}q^{5}+28q^{7}+9q^{9}-34q^{11}+\cdots\)
2496.4.a.r 2496.a 1.a $1$ $147.269$ \(\Q\) None 78.4.a.d \(0\) \(3\) \(20\) \(-32\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+20q^{5}-2^{5}q^{7}+9q^{9}-50q^{11}+\cdots\)
2496.4.a.s 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{14}) \) None 39.4.a.b \(0\) \(-6\) \(-24\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-12+\beta )q^{5}+\beta q^{7}+9q^{9}+\cdots\)
2496.4.a.t 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{10}) \) None 156.4.a.d \(0\) \(-6\) \(-24\) \(8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-12+\beta )q^{5}+(4+3\beta )q^{7}+\cdots\)
2496.4.a.u 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{43}) \) None 312.4.a.f \(0\) \(-6\) \(-12\) \(44\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-6+\beta )q^{5}+(22-\beta )q^{7}+\cdots\)
2496.4.a.v 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{113}) \) None 312.4.a.c \(0\) \(-6\) \(-6\) \(10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-3-\beta )q^{5}+(5+\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.w 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{22}) \) None 156.4.a.c \(0\) \(-6\) \(0\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+\beta q^{5}+(-4-3\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.x 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{55}) \) None 312.4.a.b \(0\) \(-6\) \(4\) \(-20\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(2+\beta )q^{5}+(-10+\beta )q^{7}+\cdots\)
2496.4.a.y 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{7}) \) None 312.4.a.e \(0\) \(-6\) \(4\) \(-20\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(2+\beta )q^{5}+(-10+3\beta )q^{7}+\cdots\)
2496.4.a.z 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{3}) \) None 312.4.a.a \(0\) \(-6\) \(4\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(2+\beta )q^{5}+(-2-3\beta )q^{7}+\cdots\)
2496.4.a.ba 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{17}) \) None 312.4.a.d \(0\) \(-6\) \(18\) \(-10\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(9-\beta )q^{5}+(-5-5\beta )q^{7}+\cdots\)
2496.4.a.bb 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{10}) \) None 156.4.a.d \(0\) \(6\) \(-24\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-12+\beta )q^{5}+(-4-3\beta )q^{7}+\cdots\)
2496.4.a.bc 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{14}) \) None 39.4.a.b \(0\) \(6\) \(-24\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-12+\beta )q^{5}-\beta q^{7}+9q^{9}+\cdots\)
2496.4.a.bd 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{43}) \) None 312.4.a.f \(0\) \(6\) \(-12\) \(-44\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-6+\beta )q^{5}+(-22+\beta )q^{7}+\cdots\)
2496.4.a.be 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{113}) \) None 312.4.a.c \(0\) \(6\) \(-6\) \(-10\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-3-\beta )q^{5}+(-5-\beta )q^{7}+\cdots\)
2496.4.a.bf 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{22}) \) None 156.4.a.c \(0\) \(6\) \(0\) \(8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+\beta q^{5}+(4+3\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.bg 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{3}) \) None 312.4.a.a \(0\) \(6\) \(4\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(2+\beta )q^{5}+(2+3\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.bh 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{7}) \) None 312.4.a.e \(0\) \(6\) \(4\) \(20\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(2+\beta )q^{5}+(10-3\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.bi 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{55}) \) None 312.4.a.b \(0\) \(6\) \(4\) \(20\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(2+\beta )q^{5}+(10-\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.bj 2496.a 1.a $2$ $147.269$ \(\Q(\sqrt{17}) \) None 312.4.a.d \(0\) \(6\) \(18\) \(10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(9-\beta )q^{5}+(5+5\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.bk 2496.a 1.a $3$ $147.269$ 3.3.36248.1 None 312.4.a.g \(0\) \(-9\) \(-16\) \(22\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-5-\beta _{2})q^{5}+(8-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2496.4.a.bl 2496.a 1.a $3$ $147.269$ 3.3.3144.1 None 39.4.a.c \(0\) \(-9\) \(-4\) \(30\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-1+\beta _{2})q^{5}+(11+3\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.bm 2496.a 1.a $3$ $147.269$ 3.3.13916.1 None 312.4.a.h \(0\) \(-9\) \(4\) \(6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(1-\beta _{2})q^{5}+(2+\beta _{1}+\beta _{2})q^{7}+\cdots\)
2496.4.a.bn 2496.a 1.a $3$ $147.269$ 3.3.3261.1 None 1248.4.a.a \(0\) \(-9\) \(10\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(3-\beta _{1})q^{5}+(-1-2\beta _{1}-\beta _{2})q^{7}+\cdots\)
2496.4.a.bo 2496.a 1.a $3$ $147.269$ 3.3.36248.1 None 312.4.a.g \(0\) \(9\) \(-16\) \(-22\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-5-\beta _{2})q^{5}+(-8+\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.bp 2496.a 1.a $3$ $147.269$ 3.3.3144.1 None 39.4.a.c \(0\) \(9\) \(-4\) \(-30\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-1+\beta _{2})q^{5}+(-11-3\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.bq 2496.a 1.a $3$ $147.269$ 3.3.13916.1 None 312.4.a.h \(0\) \(9\) \(4\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(1-\beta _{2})q^{5}+(-2-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2496.4.a.br 2496.a 1.a $3$ $147.269$ 3.3.3261.1 None 1248.4.a.a \(0\) \(9\) \(10\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(3-\beta _{1})q^{5}+(1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
2496.4.a.bs 2496.a 1.a $4$ $147.269$ 4.4.6406729.1 None 1248.4.a.d \(0\) \(-12\) \(-2\) \(18\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+\beta _{2}q^{5}+(5-\beta _{3})q^{7}+9q^{9}+\cdots\)
2496.4.a.bt 2496.a 1.a $4$ $147.269$ 4.4.236113.1 None 1248.4.a.c \(0\) \(-12\) \(2\) \(10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(1+\beta _{2})q^{5}+(3+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2496.4.a.bu 2496.a 1.a $4$ $147.269$ 4.4.6406729.1 None 1248.4.a.d \(0\) \(12\) \(-2\) \(-18\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+\beta _{2}q^{5}+(-5+\beta _{3})q^{7}+9q^{9}+\cdots\)
2496.4.a.bv 2496.a 1.a $4$ $147.269$ 4.4.236113.1 None 1248.4.a.c \(0\) \(12\) \(2\) \(-10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(1+\beta _{2})q^{5}+(-3-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
2496.4.a.bw 2496.a 1.a $5$ $147.269$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1248.4.a.k \(0\) \(-15\) \(-10\) \(-14\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-2-\beta _{2})q^{5}+(-3+\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.bx 2496.a 1.a $5$ $147.269$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1248.4.a.j \(0\) \(-15\) \(-10\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-2+\beta _{1})q^{5}-\beta _{3}q^{7}+9q^{9}+\cdots\)
2496.4.a.by 2496.a 1.a $5$ $147.269$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1248.4.a.i \(0\) \(-15\) \(-8\) \(38\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-2+\beta _{1})q^{5}+(8-\beta _{4})q^{7}+\cdots\)
2496.4.a.bz 2496.a 1.a $5$ $147.269$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1248.4.a.h \(0\) \(-15\) \(8\) \(-38\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(2+\beta _{2}-\beta _{3})q^{5}+(-7+\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.ca 2496.a 1.a $5$ $147.269$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1248.4.a.g \(0\) \(-15\) \(10\) \(-14\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(2-\beta _{2})q^{5}+(-3-\beta _{3}-\beta _{4})q^{7}+\cdots\)
2496.4.a.cb 2496.a 1.a $5$ $147.269$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1248.4.a.j \(0\) \(15\) \(-10\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-2+\beta _{1})q^{5}+\beta _{3}q^{7}+9q^{9}+\cdots\)
2496.4.a.cc 2496.a 1.a $5$ $147.269$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1248.4.a.k \(0\) \(15\) \(-10\) \(14\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-2-\beta _{2})q^{5}+(3-\beta _{1})q^{7}+\cdots\)
2496.4.a.cd 2496.a 1.a $5$ $147.269$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1248.4.a.i \(0\) \(15\) \(-8\) \(-38\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-2+\beta _{1})q^{5}+(-8+\beta _{4})q^{7}+\cdots\)
2496.4.a.ce 2496.a 1.a $5$ $147.269$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1248.4.a.h \(0\) \(15\) \(8\) \(38\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(2+\beta _{2}-\beta _{3})q^{5}+(7-\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.cf 2496.a 1.a $5$ $147.269$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1248.4.a.g \(0\) \(15\) \(10\) \(14\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(2-\beta _{2})q^{5}+(3+\beta _{3}+\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2496))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2496)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1248))\)\(^{\oplus 2}\)