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Properties

Label 1950.4.a
Level $1950$
Weight $4$
Character orbit 1950.a
Rep. character $\chi_{1950}(1,\cdot)$
Character field $\Q$
Dimension $114$
Newform subspaces $47$
Sturm bound $1680$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1950.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 47 \)
Sturm bound: \(1680\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1950))\).

Total New Old
Modular forms 1284 114 1170
Cusp forms 1236 114 1122
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.

\(2\)\(3\)\(5\)\(13\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(9\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(62\)
Minus space\(-\)\(52\)

Trace form

\( 114 q + 456 q^{4} + 12 q^{6} - 4 q^{7} + 1026 q^{9} + O(q^{10}) \) \( 114 q + 456 q^{4} + 12 q^{6} - 4 q^{7} + 1026 q^{9} - 112 q^{11} - 26 q^{13} - 40 q^{14} + 1824 q^{16} - 388 q^{17} - 4 q^{19} + 84 q^{21} + 32 q^{22} + 248 q^{23} + 48 q^{24} - 16 q^{28} + 780 q^{29} - 164 q^{31} - 336 q^{33} + 32 q^{34} + 4104 q^{36} - 276 q^{37} + 328 q^{38} - 648 q^{41} - 456 q^{42} - 80 q^{43} - 448 q^{44} - 144 q^{46} - 608 q^{47} + 5306 q^{49} + 576 q^{51} - 104 q^{52} - 1132 q^{53} + 108 q^{54} - 160 q^{56} - 156 q^{57} - 160 q^{58} - 1368 q^{59} - 460 q^{61} + 440 q^{62} - 36 q^{63} + 7296 q^{64} - 240 q^{66} - 532 q^{67} - 1552 q^{68} + 24 q^{69} - 1000 q^{71} + 1788 q^{73} - 272 q^{74} - 16 q^{76} - 2400 q^{77} - 156 q^{78} - 2256 q^{79} + 9234 q^{81} - 936 q^{82} - 1944 q^{83} + 336 q^{84} + 2544 q^{86} - 96 q^{87} + 128 q^{88} + 4224 q^{89} - 260 q^{91} + 992 q^{92} + 684 q^{93} + 1408 q^{94} + 192 q^{96} + 2012 q^{97} - 4000 q^{98} - 1008 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1950))\) 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 5 13
1950.4.a.a 1950.a 1.a $1$ $115.054$ \(\Q\) None 78.4.a.f \(-2\) \(-3\) \(0\) \(-4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-4q^{7}+\cdots\)
1950.4.a.b 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.k \(-2\) \(-3\) \(0\) \(28\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+28q^{7}+\cdots\)
1950.4.a.c 1950.a 1.a $1$ $115.054$ \(\Q\) None 78.4.a.e \(-2\) \(3\) \(0\) \(-20\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-20q^{7}+\cdots\)
1950.4.a.d 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.h \(-2\) \(3\) \(0\) \(-8\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-8q^{7}+\cdots\)
1950.4.a.e 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.i \(-2\) \(3\) \(0\) \(-8\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-8q^{7}+\cdots\)
1950.4.a.f 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.j \(-2\) \(3\) \(0\) \(12\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+12q^{7}+\cdots\)
1950.4.a.g 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.g \(-2\) \(3\) \(0\) \(25\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+5^{2}q^{7}+\cdots\)
1950.4.a.h 1950.a 1.a $1$ $115.054$ \(\Q\) None 78.4.a.d \(-2\) \(3\) \(0\) \(32\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+2^{5}q^{7}+\cdots\)
1950.4.a.i 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.e \(2\) \(-3\) \(0\) \(-24\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-24q^{7}+\cdots\)
1950.4.a.j 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.d \(2\) \(-3\) \(0\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2q^{7}+\cdots\)
1950.4.a.k 1950.a 1.a $1$ $115.054$ \(\Q\) None 78.4.a.b \(2\) \(-3\) \(0\) \(8\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+8q^{7}+\cdots\)
1950.4.a.l 1950.a 1.a $1$ $115.054$ \(\Q\) None 78.4.a.c \(2\) \(-3\) \(0\) \(8\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+8q^{7}+\cdots\)
1950.4.a.m 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.f \(2\) \(-3\) \(0\) \(13\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+13q^{7}+\cdots\)
1950.4.a.n 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.c \(2\) \(-3\) \(0\) \(15\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+15q^{7}+\cdots\)
1950.4.a.o 1950.a 1.a $1$ $115.054$ \(\Q\) None 78.4.a.a \(2\) \(3\) \(0\) \(-28\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}-28q^{7}+\cdots\)
1950.4.a.p 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.b \(2\) \(3\) \(0\) \(-5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}-5q^{7}+\cdots\)
1950.4.a.q 1950.a 1.a $1$ $115.054$ \(\Q\) None 390.4.a.a \(2\) \(3\) \(0\) \(14\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+14q^{7}+\cdots\)
1950.4.a.r 1950.a 1.a $2$ $115.054$ \(\Q(\sqrt{2193}) \) None 390.4.a.p \(-4\) \(-6\) \(0\) \(-25\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(-12+\cdots)q^{7}+\cdots\)
1950.4.a.s 1950.a 1.a $2$ $115.054$ \(\Q(\sqrt{6}) \) None 1950.4.a.s \(-4\) \(-6\) \(0\) \(14\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(7+\beta )q^{7}+\cdots\)
1950.4.a.t 1950.a 1.a $2$ $115.054$ \(\Q(\sqrt{31}) \) None 1950.4.a.t \(-4\) \(-6\) \(0\) \(24\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(12+\beta )q^{7}+\cdots\)
1950.4.a.u 1950.a 1.a $2$ $115.054$ \(\Q(\sqrt{2081}) \) None 390.4.a.o \(-4\) \(6\) \(0\) \(-27\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(-13+\cdots)q^{7}+\cdots\)
1950.4.a.v 1950.a 1.a $2$ $115.054$ \(\Q(\sqrt{139}) \) None 390.4.a.n \(4\) \(-6\) \(0\) \(12\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(6+\beta )q^{7}+\cdots\)
1950.4.a.w 1950.a 1.a $2$ $115.054$ \(\Q(\sqrt{31}) \) None 1950.4.a.t \(4\) \(6\) \(0\) \(-24\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(-12+\cdots)q^{7}+\cdots\)
1950.4.a.x 1950.a 1.a $2$ $115.054$ \(\Q(\sqrt{6}) \) None 1950.4.a.s \(4\) \(6\) \(0\) \(-14\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(-7+\cdots)q^{7}+\cdots\)
1950.4.a.y 1950.a 1.a $2$ $115.054$ \(\Q(\sqrt{129}) \) None 390.4.a.m \(4\) \(6\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(-2+\cdots)q^{7}+\cdots\)
1950.4.a.z 1950.a 1.a $2$ $115.054$ \(\Q(\sqrt{1249}) \) None 390.4.a.l \(4\) \(6\) \(0\) \(1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+\beta q^{7}+\cdots\)
1950.4.a.ba 1950.a 1.a $3$ $115.054$ 3.3.2340721.1 None 390.4.a.q \(-6\) \(-9\) \(0\) \(-17\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(-6+\cdots)q^{7}+\cdots\)
1950.4.a.bb 1950.a 1.a $3$ $115.054$ 3.3.37940.1 None 1950.4.a.bb \(-6\) \(9\) \(0\) \(-5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(-1+\cdots)q^{7}+\cdots\)
1950.4.a.bc 1950.a 1.a $3$ $115.054$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 1950.4.a.bc \(-6\) \(9\) \(0\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(-1+\cdots)q^{7}+\cdots\)
1950.4.a.bd 1950.a 1.a $3$ $115.054$ 3.3.1718836.1 None 1950.4.a.bd \(-6\) \(9\) \(0\) \(5\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(2+\beta _{2})q^{7}+\cdots\)
1950.4.a.be 1950.a 1.a $3$ $115.054$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 1950.4.a.be \(-6\) \(9\) \(0\) \(12\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(4-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bf 1950.a 1.a $3$ $115.054$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 1950.4.a.be \(6\) \(-9\) \(0\) \(-12\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(-4+\cdots)q^{7}+\cdots\)
1950.4.a.bg 1950.a 1.a $3$ $115.054$ 3.3.1718836.1 None 1950.4.a.bd \(6\) \(-9\) \(0\) \(-5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(-2+\cdots)q^{7}+\cdots\)
1950.4.a.bh 1950.a 1.a $3$ $115.054$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 1950.4.a.bc \(6\) \(-9\) \(0\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bi 1950.a 1.a $3$ $115.054$ 3.3.37940.1 None 1950.4.a.bb \(6\) \(-9\) \(0\) \(5\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bj 1950.a 1.a $4$ $115.054$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 1950.4.a.bj \(-8\) \(-12\) \(0\) \(-21\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(-5+\cdots)q^{7}+\cdots\)
1950.4.a.bk 1950.a 1.a $4$ $115.054$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 1950.4.a.bk \(-8\) \(-12\) \(0\) \(-7\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(-2+\cdots)q^{7}+\cdots\)
1950.4.a.bl 1950.a 1.a $4$ $115.054$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 390.4.e.a \(-8\) \(12\) \(0\) \(-1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1950.4.a.bm 1950.a 1.a $4$ $115.054$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 390.4.e.b \(-8\) \(12\) \(0\) \(15\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(3-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bn 1950.a 1.a $4$ $115.054$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 390.4.e.b \(8\) \(-12\) \(0\) \(-15\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(-3+\cdots)q^{7}+\cdots\)
1950.4.a.bo 1950.a 1.a $4$ $115.054$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 390.4.e.a \(8\) \(-12\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)
1950.4.a.bp 1950.a 1.a $4$ $115.054$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 1950.4.a.bk \(8\) \(12\) \(0\) \(7\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bq 1950.a 1.a $4$ $115.054$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 1950.4.a.bj \(8\) \(12\) \(0\) \(21\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(5+\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.br 1950.a 1.a $5$ $115.054$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 390.4.e.d \(-10\) \(-15\) \(0\) \(-41\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(-8+\cdots)q^{7}+\cdots\)
1950.4.a.bs 1950.a 1.a $5$ $115.054$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 390.4.e.c \(-10\) \(-15\) \(0\) \(27\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(6-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.4.a.bt 1950.a 1.a $5$ $115.054$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 390.4.e.c \(10\) \(15\) \(0\) \(-27\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(-6+\cdots)q^{7}+\cdots\)
1950.4.a.bu 1950.a 1.a $5$ $115.054$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 390.4.e.d \(10\) \(15\) \(0\) \(41\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+(8-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1950))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1950)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(650))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(975))\)\(^{\oplus 2}\)