Properties

Label 9405.2.a
Level $9405$
Weight $2$
Character orbit 9405.a
Rep. character $\chi_{9405}(1,\cdot)$
Character field $\Q$
Dimension $300$
Newform subspaces $48$
Sturm bound $2880$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 9405 = 3^{2} \cdot 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9405.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 48 \)
Sturm bound: \(2880\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9405))\).

Total New Old
Modular forms 1456 300 1156
Cusp forms 1425 300 1125
Eisenstein series 31 0 31

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

\(3\)\(5\)\(11\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)\(15\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(19\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(15\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(11\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(15\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(19\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(23\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(21\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(23\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(25\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(22\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(24\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(22\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(20\)
Plus space\(+\)\(138\)
Minus space\(-\)\(162\)

Trace form

\( 300 q + 300 q^{4} - 4 q^{5} - 24 q^{8} + O(q^{10}) \) \( 300 q + 300 q^{4} - 4 q^{5} - 24 q^{8} - 40 q^{14} + 308 q^{16} - 4 q^{20} - 24 q^{23} + 300 q^{25} - 16 q^{26} - 16 q^{29} + 8 q^{31} - 88 q^{32} + 8 q^{34} + 8 q^{35} - 12 q^{38} + 8 q^{41} - 24 q^{43} + 8 q^{44} - 8 q^{46} - 48 q^{47} + 340 q^{49} + 72 q^{52} + 16 q^{53} + 8 q^{55} - 80 q^{56} + 48 q^{58} + 8 q^{59} + 40 q^{61} + 16 q^{62} + 412 q^{64} + 8 q^{65} - 24 q^{67} - 16 q^{68} + 32 q^{70} + 40 q^{71} - 16 q^{73} + 16 q^{74} - 8 q^{77} - 8 q^{79} - 12 q^{80} + 112 q^{82} - 40 q^{83} + 8 q^{85} - 40 q^{89} + 16 q^{91} + 48 q^{92} + 152 q^{94} - 40 q^{97} + 104 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9405))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 11 19
9405.2.a.a 9405.a 1.a $1$ $75.099$ \(\Q\) None 3135.2.a.h \(-2\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-2q^{7}-2q^{10}+\cdots\)
9405.2.a.b 9405.a 1.a $1$ $75.099$ \(\Q\) None 9405.2.a.b \(-2\) \(0\) \(1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-2q^{10}-q^{11}+\cdots\)
9405.2.a.c 9405.a 1.a $1$ $75.099$ \(\Q\) None 9405.2.a.c \(-2\) \(0\) \(1\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}+4q^{7}-2q^{10}+\cdots\)
9405.2.a.d 9405.a 1.a $1$ $75.099$ \(\Q\) None 1045.2.a.b \(-1\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+q^{11}+\cdots\)
9405.2.a.e 9405.a 1.a $1$ $75.099$ \(\Q\) None 3135.2.a.g \(-1\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
9405.2.a.f 9405.a 1.a $1$ $75.099$ \(\Q\) None 3135.2.a.f \(-1\) \(0\) \(-1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
9405.2.a.g 9405.a 1.a $1$ $75.099$ \(\Q\) None 3135.2.a.c \(1\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-q^{11}+\cdots\)
9405.2.a.h 9405.a 1.a $1$ $75.099$ \(\Q\) None 3135.2.a.e \(1\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+q^{11}+\cdots\)
9405.2.a.i 9405.a 1.a $1$ $75.099$ \(\Q\) None 3135.2.a.b \(1\) \(0\) \(1\) \(-4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots\)
9405.2.a.j 9405.a 1.a $1$ $75.099$ \(\Q\) None 1045.2.a.a \(1\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
9405.2.a.k 9405.a 1.a $1$ $75.099$ \(\Q\) None 3135.2.a.d \(1\) \(0\) \(1\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
9405.2.a.l 9405.a 1.a $1$ $75.099$ \(\Q\) None 3135.2.a.a \(2\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-2q^{7}-2q^{10}+\cdots\)
9405.2.a.m 9405.a 1.a $1$ $75.099$ \(\Q\) None 9405.2.a.b \(2\) \(0\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-2q^{10}+q^{11}+\cdots\)
9405.2.a.n 9405.a 1.a $1$ $75.099$ \(\Q\) None 9405.2.a.c \(2\) \(0\) \(-1\) \(4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}+4q^{7}-2q^{10}+\cdots\)
9405.2.a.o 9405.a 1.a $2$ $75.099$ \(\Q(\sqrt{2}) \) None 1045.2.a.c \(-2\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}+2\beta q^{7}+\cdots\)
9405.2.a.p 9405.a 1.a $3$ $75.099$ \(\Q(\zeta_{18})^+\) None 3135.2.a.k \(0\) \(0\) \(-3\) \(-3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
9405.2.a.q 9405.a 1.a $3$ $75.099$ \(\Q(\zeta_{18})^+\) None 3135.2.a.l \(0\) \(0\) \(-3\) \(-3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
9405.2.a.r 9405.a 1.a $3$ $75.099$ \(\Q(\zeta_{14})^+\) None 3135.2.a.j \(2\) \(0\) \(-3\) \(-5\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
9405.2.a.s 9405.a 1.a $3$ $75.099$ \(\Q(\zeta_{14})^+\) None 3135.2.a.i \(2\) \(0\) \(3\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
9405.2.a.t 9405.a 1.a $4$ $75.099$ 4.4.132889.1 None 3135.2.a.m \(1\) \(0\) \(-4\) \(-5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
9405.2.a.u 9405.a 1.a $5$ $75.099$ 5.5.36497.1 None 1045.2.a.e \(1\) \(0\) \(5\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+\beta _{3}q^{4}+q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
9405.2.a.v 9405.a 1.a $5$ $75.099$ \(\Q(\zeta_{22})^+\) None 1045.2.a.d \(3\) \(0\) \(-5\) \(-11\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{3}-\beta _{4})q^{2}+(1+\beta _{1}+\beta _{4})q^{4}+\cdots\)
9405.2.a.w 9405.a 1.a $6$ $75.099$ 6.6.131947641.1 None 1045.2.a.g \(0\) \(0\) \(-6\) \(5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2}-\beta _{3})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
9405.2.a.x 9405.a 1.a $6$ $75.099$ 6.6.905177.1 None 3135.2.a.p \(1\) \(0\) \(-6\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1+\beta _{1})q^{4}-q^{5}-\beta _{5}q^{7}+\cdots\)
9405.2.a.y 9405.a 1.a $6$ $75.099$ 6.6.20413244.1 None 3135.2.a.o \(2\) \(0\) \(6\) \(-7\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
9405.2.a.z 9405.a 1.a $6$ $75.099$ 6.6.7281497.1 None 1045.2.a.f \(2\) \(0\) \(6\) \(5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
9405.2.a.ba 9405.a 1.a $6$ $75.099$ 6.6.31252925.1 None 3135.2.a.n \(2\) \(0\) \(6\) \(5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
9405.2.a.bb 9405.a 1.a $7$ $75.099$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 3135.2.a.s \(-3\) \(0\) \(7\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
9405.2.a.bc 9405.a 1.a $7$ $75.099$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 3135.2.a.r \(-1\) \(0\) \(-7\) \(4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+\beta _{6}q^{4}-q^{5}+(-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
9405.2.a.bd 9405.a 1.a $7$ $75.099$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 1045.2.a.h \(-1\) \(0\) \(7\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
9405.2.a.be 9405.a 1.a $7$ $75.099$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 3135.2.a.q \(3\) \(0\) \(7\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
9405.2.a.bf 9405.a 1.a $8$ $75.099$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1045.2.a.i \(6\) \(0\) \(-8\) \(-11\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
9405.2.a.bg 9405.a 1.a $9$ $75.099$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 3135.2.a.w \(-5\) \(0\) \(-9\) \(5\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9405.2.a.bh 9405.a 1.a $9$ $75.099$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 1045.2.a.k \(-3\) \(0\) \(-9\) \(13\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots\)
9405.2.a.bi 9405.a 1.a $9$ $75.099$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 1045.2.a.j \(-3\) \(0\) \(9\) \(-9\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{8})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
9405.2.a.bj 9405.a 1.a $9$ $75.099$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 3135.2.a.v \(-3\) \(0\) \(9\) \(3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\beta _{7}q^{7}+\cdots\)
9405.2.a.bk 9405.a 1.a $9$ $75.099$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 3135.2.a.u \(-2\) \(0\) \(-9\) \(-3\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{6}q^{7}+\cdots\)
9405.2.a.bl 9405.a 1.a $9$ $75.099$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 3135.2.a.t \(1\) \(0\) \(9\) \(7\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{6}+\cdots)q^{7}+\cdots\)
9405.2.a.bm 9405.a 1.a $10$ $75.099$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 3135.2.a.x \(-4\) \(0\) \(10\) \(5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+\beta _{7}q^{7}+\cdots\)
9405.2.a.bn 9405.a 1.a $10$ $75.099$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 9405.2.a.bn \(-1\) \(0\) \(-10\) \(-8\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1+\beta _{8}+\cdots)q^{7}+\cdots\)
9405.2.a.bo 9405.a 1.a $10$ $75.099$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 9405.2.a.bn \(1\) \(0\) \(10\) \(-8\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1+\beta _{8}+\cdots)q^{7}+\cdots\)
9405.2.a.bp 9405.a 1.a $12$ $75.099$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 3135.2.a.y \(-1\) \(0\) \(-12\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+\beta _{4}q^{7}+\cdots\)
9405.2.a.bq 9405.a 1.a $14$ $75.099$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 9405.2.a.bq \(-1\) \(0\) \(14\) \(-12\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
9405.2.a.br 9405.a 1.a $14$ $75.099$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 9405.2.a.bq \(1\) \(0\) \(-14\) \(-12\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
9405.2.a.bs 9405.a 1.a $15$ $75.099$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 9405.2.a.bs \(-1\) \(0\) \(-15\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{9}q^{7}+\cdots\)
9405.2.a.bt 9405.a 1.a $15$ $75.099$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 9405.2.a.bs \(1\) \(0\) \(15\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{9}q^{7}+\cdots\)
9405.2.a.bu 9405.a 1.a $19$ $75.099$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None 9405.2.a.bu \(-3\) \(0\) \(-19\) \(12\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1-\beta _{8}+\cdots)q^{7}+\cdots\)
9405.2.a.bv 9405.a 1.a $19$ $75.099$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None 9405.2.a.bu \(3\) \(0\) \(19\) \(12\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9405))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9405)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(627))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1045))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1881))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3135))\)\(^{\oplus 2}\)