Properties

Label 2475.4.a
Level $2475$
Weight $4$
Character orbit 2475.a
Rep. character $\chi_{2475}(1,\cdot)$
Character field $\Q$
Dimension $238$
Newform subspaces $53$
Sturm bound $1440$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2475.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 53 \)
Sturm bound: \(1440\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2475))\).

Total New Old
Modular forms 1104 238 866
Cusp forms 1056 238 818
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.

\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(22\)
\(+\)\(+\)\(-\)\(-\)\(22\)
\(+\)\(-\)\(+\)\(-\)\(26\)
\(+\)\(-\)\(-\)\(+\)\(26\)
\(-\)\(+\)\(+\)\(-\)\(33\)
\(-\)\(+\)\(-\)\(+\)\(35\)
\(-\)\(-\)\(+\)\(+\)\(39\)
\(-\)\(-\)\(-\)\(-\)\(35\)
Plus space\(+\)\(122\)
Minus space\(-\)\(116\)

Trace form

\( 238 q - 2 q^{2} + 944 q^{4} - 44 q^{7} + 12 q^{8} + O(q^{10}) \) \( 238 q - 2 q^{2} + 944 q^{4} - 44 q^{7} + 12 q^{8} - 22 q^{11} - 20 q^{13} + 68 q^{14} + 3920 q^{16} - 36 q^{17} + 32 q^{19} - 22 q^{22} + 354 q^{23} - 1252 q^{26} - 1500 q^{28} - 156 q^{29} + 270 q^{31} - 956 q^{32} + 500 q^{34} - 86 q^{37} + 824 q^{38} - 124 q^{41} + 260 q^{43} - 528 q^{44} + 1102 q^{46} + 524 q^{47} + 12182 q^{49} - 484 q^{52} + 112 q^{53} + 408 q^{56} - 1056 q^{58} - 1406 q^{59} - 1848 q^{61} - 730 q^{62} + 13372 q^{64} - 3162 q^{67} - 2068 q^{68} + 978 q^{71} - 1052 q^{73} + 5982 q^{74} + 2980 q^{76} + 396 q^{77} + 3500 q^{79} + 5160 q^{82} - 1612 q^{83} + 1776 q^{86} + 132 q^{88} + 258 q^{89} - 840 q^{91} + 1028 q^{92} + 6336 q^{94} - 3418 q^{97} - 2266 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2475))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 11
2475.4.a.a 2475.a 1.a $1$ $146.030$ \(\Q\) None \(-5\) \(0\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-5q^{2}+17q^{4}+3q^{7}-45q^{8}+11q^{11}+\cdots\)
2475.4.a.b 2475.a 1.a $1$ $146.030$ \(\Q\) None \(-5\) \(0\) \(0\) \(32\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-5q^{2}+17q^{4}+2^{5}q^{7}-45q^{8}+11q^{11}+\cdots\)
2475.4.a.c 2475.a 1.a $1$ $146.030$ \(\Q\) None \(-4\) \(0\) \(0\) \(-21\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+8q^{4}-21q^{7}-11q^{11}+68q^{13}+\cdots\)
2475.4.a.d 2475.a 1.a $1$ $146.030$ \(\Q\) None \(-3\) \(0\) \(0\) \(7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}+7q^{7}+21q^{8}-11q^{11}+\cdots\)
2475.4.a.e 2475.a 1.a $1$ $146.030$ \(\Q\) None \(-1\) \(0\) \(0\) \(26\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}+26q^{7}+15q^{8}-11q^{11}+\cdots\)
2475.4.a.f 2475.a 1.a $1$ $146.030$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-8q^{4}-2q^{7}+11q^{11}+22q^{13}+\cdots\)
2475.4.a.g 2475.a 1.a $1$ $146.030$ \(\Q\) None \(1\) \(0\) \(0\) \(-36\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-7q^{4}-6^{2}q^{7}-15q^{8}-11q^{11}+\cdots\)
2475.4.a.h 2475.a 1.a $1$ $146.030$ \(\Q\) None \(1\) \(0\) \(0\) \(9\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-7q^{4}+9q^{7}-15q^{8}-11q^{11}+\cdots\)
2475.4.a.i 2475.a 1.a $1$ $146.030$ \(\Q\) None \(3\) \(0\) \(0\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{2}+q^{4}-7q^{7}-21q^{8}-11q^{11}+\cdots\)
2475.4.a.j 2475.a 1.a $1$ $146.030$ \(\Q\) None \(4\) \(0\) \(0\) \(21\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+8q^{4}+21q^{7}-11q^{11}-68q^{13}+\cdots\)
2475.4.a.k 2475.a 1.a $1$ $146.030$ \(\Q\) None \(5\) \(0\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+5q^{2}+17q^{4}-3q^{7}+45q^{8}+11q^{11}+\cdots\)
2475.4.a.l 2475.a 1.a $2$ $146.030$ \(\Q(\sqrt{17}) \) None \(-7\) \(0\) \(0\) \(25\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-3-\beta )q^{2}+(5+7\beta )q^{4}+(17-9\beta )q^{7}+\cdots\)
2475.4.a.m 2475.a 1.a $2$ $146.030$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(16\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(5-2\beta )q^{4}+(8+5\beta )q^{7}+\cdots\)
2475.4.a.n 2475.a 1.a $2$ $146.030$ \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-4+\beta )q^{4}+(4-4\beta )q^{7}+\cdots\)
2475.4.a.o 2475.a 1.a $2$ $146.030$ \(\Q(\sqrt{33}) \) None \(1\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{4}+(-2+2\beta )q^{7}+(8-7\beta )q^{8}+\cdots\)
2475.4.a.p 2475.a 1.a $2$ $146.030$ \(\Q(\sqrt{97}) \) None \(1\) \(0\) \(0\) \(-24\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2^{4}+\beta )q^{4}+(-14+4\beta )q^{7}+\cdots\)
2475.4.a.q 2475.a 1.a $2$ $146.030$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(-20\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-4+2\beta )q^{4}+(-10+\cdots)q^{7}+\cdots\)
2475.4.a.r 2475.a 1.a $2$ $146.030$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(16\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(5+2\beta )q^{4}+(8-5\beta )q^{7}+\cdots\)
2475.4.a.s 2475.a 1.a $3$ $146.030$ 3.3.23612.1 None \(-4\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(7+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2475.4.a.t 2475.a 1.a $3$ $146.030$ 3.3.47528.1 None \(-2\) \(0\) \(0\) \(-10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(10+\beta _{2})q^{4}+(-4+\cdots)q^{7}+\cdots\)
2475.4.a.u 2475.a 1.a $3$ $146.030$ 3.3.1772.1 None \(-1\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+2\beta _{2})q^{4}+(-2+4\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.v 2475.a 1.a $3$ $146.030$ 3.3.3368.1 None \(-1\) \(0\) \(0\) \(16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(3+2\beta _{2})q^{4}+(7-4\beta _{1}+\beta _{2})q^{7}+\cdots\)
2475.4.a.w 2475.a 1.a $3$ $146.030$ 3.3.788.1 None \(1\) \(0\) \(0\) \(16\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(-2-\beta _{1})q^{4}+(3-5\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.x 2475.a 1.a $3$ $146.030$ 3.3.1772.1 None \(1\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+2\beta _{2})q^{4}+(-2+4\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.y 2475.a 1.a $3$ $146.030$ 3.3.3368.1 None \(1\) \(0\) \(0\) \(-16\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(3+2\beta _{2})q^{4}+(-7+4\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.z 2475.a 1.a $3$ $146.030$ 3.3.1957.1 None \(1\) \(0\) \(0\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(6+\beta _{1}+2\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
2475.4.a.ba 2475.a 1.a $3$ $146.030$ 3.3.568.1 None \(5\) \(0\) \(0\) \(15\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}-\beta _{2})q^{2}+(7+2\beta _{1})q^{4}+(8+\cdots)q^{7}+\cdots\)
2475.4.a.bb 2475.a 1.a $4$ $146.030$ 4.4.91035289.2 None \(-2\) \(0\) \(0\) \(11\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(-4-\beta _{3})q^{4}+(3-\beta _{2}+\beta _{3})q^{7}+\cdots\)
2475.4.a.bc 2475.a 1.a $4$ $146.030$ 4.4.1539480.1 None \(1\) \(0\) \(0\) \(-9\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(5+\beta _{1}+\beta _{3})q^{4}+(-2+2\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.bd 2475.a 1.a $4$ $146.030$ 4.4.91035289.2 None \(2\) \(0\) \(0\) \(-11\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(-4-\beta _{3})q^{4}+(-3-\beta _{2}+\cdots)q^{7}+\cdots\)
2475.4.a.be 2475.a 1.a $4$ $146.030$ 4.4.1540841.1 None \(4\) \(0\) \(0\) \(-34\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(7-\beta _{1}+\beta _{3})q^{4}+(-8+\cdots)q^{7}+\cdots\)
2475.4.a.bf 2475.a 1.a $5$ $146.030$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-4\) \(0\) \(0\) \(-38\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(9-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2475.4.a.bg 2475.a 1.a $5$ $146.030$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-2\) \(0\) \(0\) \(24\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(5+\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.bh 2475.a 1.a $5$ $146.030$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-2\) \(0\) \(0\) \(40\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(8+\beta _{2}+\beta _{3})q^{4}+(9-2\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.bi 2475.a 1.a $5$ $146.030$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-1\) \(0\) \(0\) \(18\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(4+\beta _{2}-\beta _{4})q^{7}+\cdots\)
2475.4.a.bj 2475.a 1.a $5$ $146.030$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(0\) \(0\) \(-18\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-4-\beta _{2}+\beta _{4})q^{7}+\cdots\)
2475.4.a.bk 2475.a 1.a $5$ $146.030$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(2\) \(0\) \(0\) \(-24\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-5-\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.bl 2475.a 1.a $5$ $146.030$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(2\) \(0\) \(0\) \(-40\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(8+\beta _{2}+\beta _{3})q^{4}+(-9+2\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.bm 2475.a 1.a $5$ $146.030$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(4\) \(0\) \(0\) \(38\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(9-\beta _{1}+\beta _{2})q^{4}+(7+\cdots)q^{7}+\cdots\)
2475.4.a.bn 2475.a 1.a $6$ $146.030$ 6.6.2301792529.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
2475.4.a.bo 2475.a 1.a $7$ $146.030$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-5\) \(0\) \(0\) \(34\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
2475.4.a.bp 2475.a 1.a $7$ $146.030$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-5\) \(0\) \(0\) \(-30\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(5-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2475.4.a.bq 2475.a 1.a $7$ $146.030$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(0\) \(0\) \(50\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(6+\beta _{2})q^{4}+(7+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2475.4.a.br 2475.a 1.a $7$ $146.030$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(0\) \(0\) \(-50\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(6+\beta _{2})q^{4}+(-7-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
2475.4.a.bs 2475.a 1.a $7$ $146.030$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(5\) \(0\) \(0\) \(-34\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-2\beta _{1}+\beta _{2})q^{4}+(-5+\cdots)q^{7}+\cdots\)
2475.4.a.bt 2475.a 1.a $7$ $146.030$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(5\) \(0\) \(0\) \(-30\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(5-\beta _{1}+\beta _{2})q^{4}+(-4+\cdots)q^{7}+\cdots\)
2475.4.a.bu 2475.a 1.a $10$ $146.030$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.bv 2475.a 1.a $10$ $146.030$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.bw 2475.a 1.a $10$ $146.030$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(6+\beta _{2})q^{4}+(\beta _{6}+\beta _{7})q^{7}+\cdots\)
2475.4.a.bx 2475.a 1.a $10$ $146.030$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.by 2475.a 1.a $10$ $146.030$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
2475.4.a.bz 2475.a 1.a $16$ $146.030$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(-\beta _{1}-\beta _{12}+\cdots)q^{7}+\cdots\)
2475.4.a.ca 2475.a 1.a $16$ $146.030$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(\beta _{1}+\beta _{12})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2475))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2475)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(825))\)\(^{\oplus 2}\)