Properties

Label 5400.2.a
Level $5400$
Weight $2$
Character orbit 5400.a
Rep. character $\chi_{5400}(1,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $60$
Sturm bound $2160$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5400.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 60 \)
Sturm bound: \(2160\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5400))\).

Total New Old
Modular forms 1152 76 1076
Cusp forms 1009 76 933
Eisenstein series 143 0 143

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

\(2\)\(3\)\(5\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(10\)
\(-\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(12\)
Plus space\(+\)\(35\)
Minus space\(-\)\(41\)

Trace form

\( 76 q + 4 q^{7} + O(q^{10}) \) \( 76 q + 4 q^{7} - 6 q^{13} + 2 q^{19} - 10 q^{31} + 26 q^{37} - 20 q^{43} + 68 q^{49} + 22 q^{61} - 6 q^{67} - 8 q^{73} + 10 q^{79} - 18 q^{91} - 20 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5400))\) 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
5400.2.a.a 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.a \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-4q^{11}+q^{13}-8q^{17}-8q^{19}+\cdots\)
5400.2.a.b 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.f.b \(0\) \(0\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-q^{11}+q^{13}+3q^{17}+2q^{19}+\cdots\)
5400.2.a.c 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.f.b \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}+q^{11}+q^{13}-3q^{17}+2q^{19}+\cdots\)
5400.2.a.d 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.a \(0\) \(0\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}+4q^{11}+q^{13}+8q^{17}-8q^{19}+\cdots\)
5400.2.a.e 5400.a 1.a $1$ $43.119$ \(\Q\) None 216.2.a.b \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{7}-5q^{11}-4q^{13}-8q^{17}+2q^{19}+\cdots\)
5400.2.a.f 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.f \(0\) \(0\) \(0\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{7}-4q^{11}+6q^{13}-6q^{17}-q^{19}+\cdots\)
5400.2.a.g 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.f \(0\) \(0\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{7}+4q^{11}+6q^{13}+6q^{17}-q^{19}+\cdots\)
5400.2.a.h 5400.a 1.a $1$ $43.119$ \(\Q\) None 216.2.a.b \(0\) \(0\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{7}+5q^{11}-4q^{13}+8q^{17}+2q^{19}+\cdots\)
5400.2.a.i 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.i \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-5q^{11}-q^{13}-2q^{17}-8q^{19}+\cdots\)
5400.2.a.j 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.e \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-4q^{11}+2q^{13}+5q^{17}-5q^{19}+\cdots\)
5400.2.a.k 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.k \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{11}-3q^{13}+2q^{17}+4q^{19}+\cdots\)
5400.2.a.l 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.f.a \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-2q^{11}+2q^{13}+3q^{17}-q^{19}+\cdots\)
5400.2.a.m 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.f \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-q^{11}-q^{13}-q^{17}+4q^{19}+\cdots\)
5400.2.a.n 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.f \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+q^{11}-q^{13}+q^{17}+4q^{19}+\cdots\)
5400.2.a.o 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.f.a \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+2q^{11}+2q^{13}-3q^{17}-q^{19}+\cdots\)
5400.2.a.p 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.k \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+3q^{11}-3q^{13}-2q^{17}+4q^{19}+\cdots\)
5400.2.a.q 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.e \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+4q^{11}+2q^{13}-5q^{17}-5q^{19}+\cdots\)
5400.2.a.r 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.i \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+5q^{11}-q^{13}+2q^{17}-8q^{19}+\cdots\)
5400.2.a.s 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.s \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-6q^{11}-6q^{13}+2q^{17}+7q^{19}+\cdots\)
5400.2.a.t 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.t \(0\) \(0\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}-2q^{11}-2q^{13}+2q^{17}+q^{19}+\cdots\)
5400.2.a.u 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.t \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}+2q^{11}-2q^{13}-2q^{17}+q^{19}+\cdots\)
5400.2.a.v 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.s \(0\) \(0\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}+6q^{11}-6q^{13}-2q^{17}+7q^{19}+\cdots\)
5400.2.a.w 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.d \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{11}+3q^{17}-q^{19}+3q^{23}-4q^{29}+\cdots\)
5400.2.a.x 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.d \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{11}-3q^{17}-q^{19}-3q^{23}+4q^{29}+\cdots\)
5400.2.a.y 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.s \(0\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-6q^{11}+6q^{13}-2q^{17}+7q^{19}+\cdots\)
5400.2.a.z 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.t \(0\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{11}+2q^{13}-2q^{17}+q^{19}+\cdots\)
5400.2.a.ba 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.c \(0\) \(0\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{11}+5q^{13}+4q^{17}-5q^{19}+\cdots\)
5400.2.a.bb 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.t \(0\) \(0\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}+2q^{11}+2q^{13}+2q^{17}+q^{19}+\cdots\)
5400.2.a.bc 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.c \(0\) \(0\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}+2q^{11}+5q^{13}-4q^{17}-5q^{19}+\cdots\)
5400.2.a.bd 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.s \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+6q^{11}+6q^{13}+2q^{17}+7q^{19}+\cdots\)
5400.2.a.be 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.i \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-5q^{11}+q^{13}+2q^{17}-8q^{19}+\cdots\)
5400.2.a.bf 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.k \(0\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{11}+3q^{13}-2q^{17}+4q^{19}+\cdots\)
5400.2.a.bg 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.f.a \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-2q^{11}-2q^{13}-3q^{17}-q^{19}+\cdots\)
5400.2.a.bh 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.b \(0\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}+6q^{13}-7q^{17}+7q^{19}-7q^{23}+\cdots\)
5400.2.a.bi 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.b \(0\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}+6q^{13}+7q^{17}+7q^{19}+7q^{23}+\cdots\)
5400.2.a.bj 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.f.a \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+2q^{11}-2q^{13}+3q^{17}-q^{19}+\cdots\)
5400.2.a.bk 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.k \(0\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}+3q^{11}+3q^{13}+2q^{17}+4q^{19}+\cdots\)
5400.2.a.bl 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.i \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+5q^{11}+q^{13}-2q^{17}-8q^{19}+\cdots\)
5400.2.a.bm 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.f \(0\) \(0\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{7}-4q^{11}-6q^{13}+6q^{17}-q^{19}+\cdots\)
5400.2.a.bn 5400.a 1.a $1$ $43.119$ \(\Q\) None 216.2.a.a \(0\) \(0\) \(0\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{7}-4q^{11}-q^{13}-4q^{17}-q^{19}+\cdots\)
5400.2.a.bo 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.f \(0\) \(0\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{7}+4q^{11}-6q^{13}-6q^{17}-q^{19}+\cdots\)
5400.2.a.bp 5400.a 1.a $1$ $43.119$ \(\Q\) None 216.2.a.a \(0\) \(0\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{7}+4q^{11}-q^{13}+4q^{17}-q^{19}+\cdots\)
5400.2.a.bq 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.a \(0\) \(0\) \(0\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-4q^{11}-q^{13}+8q^{17}-8q^{19}+\cdots\)
5400.2.a.br 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.a \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-2q^{11}-4q^{13}+q^{17}-5q^{19}+\cdots\)
5400.2.a.bs 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.f.b \(0\) \(0\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-q^{11}-q^{13}-3q^{17}+2q^{19}+\cdots\)
5400.2.a.bt 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.f.b \(0\) \(0\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}+q^{11}-q^{13}+3q^{17}+2q^{19}+\cdots\)
5400.2.a.bu 5400.a 1.a $1$ $43.119$ \(\Q\) None 1080.2.a.a \(0\) \(0\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}+2q^{11}-4q^{13}-q^{17}-5q^{19}+\cdots\)
5400.2.a.bv 5400.a 1.a $1$ $43.119$ \(\Q\) None 5400.2.a.a \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}+4q^{11}-q^{13}-8q^{17}-8q^{19}+\cdots\)
5400.2.a.bw 5400.a 1.a $2$ $43.119$ \(\Q(\sqrt{6}) \) None 1080.2.f.e \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}+(-2-\beta )q^{11}+(1+2\beta )q^{13}+\cdots\)
5400.2.a.bx 5400.a 1.a $2$ $43.119$ \(\Q(\sqrt{13}) \) None 5400.2.a.bx \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{7}-q^{11}+(-2+\beta )q^{13}+\cdots\)
5400.2.a.by 5400.a 1.a $2$ $43.119$ \(\Q(\sqrt{13}) \) None 5400.2.a.bx \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{7}+q^{11}+(-2+\beta )q^{13}+\cdots\)
5400.2.a.bz 5400.a 1.a $2$ $43.119$ \(\Q(\sqrt{6}) \) None 1080.2.f.e \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}+(2+\beta )q^{11}+(1+2\beta )q^{13}+2\beta q^{17}+\cdots\)
5400.2.a.ca 5400.a 1.a $2$ $43.119$ \(\Q(\sqrt{73}) \) None 1080.2.a.m \(0\) \(0\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{7}+(-1+\beta )q^{11}-3q^{13}+(-3+\cdots)q^{17}+\cdots\)
5400.2.a.cb 5400.a 1.a $2$ $43.119$ \(\Q(\sqrt{73}) \) None 1080.2.a.m \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{7}+(1-\beta )q^{11}-3q^{13}+(3-\beta )q^{17}+\cdots\)
5400.2.a.cc 5400.a 1.a $2$ $43.119$ \(\Q(\sqrt{6}) \) None 1080.2.f.e \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+(-2-\beta )q^{11}+(-1-2\beta )q^{13}+\cdots\)
5400.2.a.cd 5400.a 1.a $2$ $43.119$ \(\Q(\sqrt{13}) \) None 5400.2.a.bx \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{7}-q^{11}+(2-\beta )q^{13}+(-1+\cdots)q^{17}+\cdots\)
5400.2.a.ce 5400.a 1.a $2$ $43.119$ \(\Q(\sqrt{13}) \) None 5400.2.a.bx \(0\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{7}+q^{11}+(2-\beta )q^{13}+(1+\cdots)q^{17}+\cdots\)
5400.2.a.cf 5400.a 1.a $2$ $43.119$ \(\Q(\sqrt{6}) \) None 1080.2.f.e \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+(2-\beta )q^{11}+(-1+2\beta )q^{13}+\cdots\)
5400.2.a.cg 5400.a 1.a $4$ $43.119$ \(\Q(\sqrt{3}, \sqrt{19})\) None 1080.2.f.g \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{7}+(-\beta _{1}-2\beta _{2})q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
5400.2.a.ch 5400.a 1.a $4$ $43.119$ \(\Q(\sqrt{3}, \sqrt{19})\) None 1080.2.f.g \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{7}+(\beta _{1}+2\beta _{2})q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5400)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(675))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(900))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1350))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2700))\)\(^{\oplus 2}\)