Properties

Label 7920.2.a
Level $7920$
Weight $2$
Character orbit 7920.a
Rep. character $\chi_{7920}(1,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $66$
Sturm bound $3456$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7920.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 66 \)
Sturm bound: \(3456\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(13\), \(17\), \(19\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7920))\).

Total New Old
Modular forms 1776 100 1676
Cusp forms 1681 100 1581
Eisenstein series 95 0 95

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

\(2\)\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(44\)
Minus space\(-\)\(56\)

Trace form

\( 100q + 8q^{7} + O(q^{10}) \) \( 100q + 8q^{7} - 12q^{23} + 100q^{25} - 8q^{29} - 24q^{31} - 16q^{43} - 20q^{47} + 116q^{49} + 4q^{55} - 16q^{59} + 16q^{61} - 4q^{67} - 16q^{71} + 16q^{73} - 64q^{83} + 16q^{85} + 16q^{89} + 24q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7920))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 11
7920.2.a.a \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}-4q^{7}-q^{11}-4q^{13}+2q^{17}+\cdots\)
7920.2.a.b \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-4q^{7}-q^{11}+6q^{13}+6q^{17}+\cdots\)
7920.2.a.c \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}-4q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
7920.2.a.d \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}-3q^{7}+q^{11}-6q^{13}+7q^{17}+\cdots\)
7920.2.a.e \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}-q^{11}-6q^{13}-3q^{17}+\cdots\)
7920.2.a.f \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
7920.2.a.g \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
7920.2.a.h \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{11}-2q^{13}+6q^{17}+4q^{19}+\cdots\)
7920.2.a.i \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
7920.2.a.j \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{11}-6q^{13}+6q^{17}+q^{25}+\cdots\)
7920.2.a.k \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{11}-2q^{17}-2q^{19}+6q^{23}+\cdots\)
7920.2.a.l \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{11}+4q^{17}+4q^{19}+6q^{23}+\cdots\)
7920.2.a.m \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{11}+6q^{13}-2q^{17}+4q^{19}+\cdots\)
7920.2.a.n \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}+4q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots\)
7920.2.a.o \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+4q^{7}-q^{11}-4q^{13}+4q^{19}+\cdots\)
7920.2.a.p \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}+4q^{7}-q^{11}+2q^{13}-6q^{17}+\cdots\)
7920.2.a.q \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+4q^{7}+q^{11}-6q^{13}+2q^{17}+\cdots\)
7920.2.a.r \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+4q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots\)
7920.2.a.s \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(-5\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}-5q^{7}+q^{11}+2q^{13}-3q^{17}+\cdots\)
7920.2.a.t \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-4q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
7920.2.a.u \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-4q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
7920.2.a.v \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(-4\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}-4q^{7}+q^{11}-4q^{13}-2q^{17}+\cdots\)
7920.2.a.w \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-2q^{7}-q^{11}-4q^{13}+4q^{19}+\cdots\)
7920.2.a.x \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}-2q^{7}+q^{11}-4q^{17}+4q^{19}+\cdots\)
7920.2.a.y \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}-2q^{7}+q^{11}+2q^{13}-2q^{19}+\cdots\)
7920.2.a.z \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{11}+2q^{17}-2q^{19}-6q^{23}+\cdots\)
7920.2.a.ba \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{11}-4q^{13}+2q^{17}-2q^{19}+\cdots\)
7920.2.a.bb \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{11}+2q^{13}+2q^{17}-8q^{19}+\cdots\)
7920.2.a.bc \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+q^{7}-q^{11}+2q^{13}+3q^{17}+\cdots\)
7920.2.a.bd \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}+2q^{7}-q^{11}-4q^{13}-4q^{17}+\cdots\)
7920.2.a.be \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}+2q^{7}-q^{11}-4q^{13}+4q^{17}+\cdots\)
7920.2.a.bf \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}+2q^{7}-q^{11}-4q^{17}-4q^{19}+\cdots\)
7920.2.a.bg \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}+2q^{7}-q^{11}+8q^{19}-8q^{23}+\cdots\)
7920.2.a.bh \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+2q^{7}-q^{11}+2q^{13}-8q^{17}+\cdots\)
7920.2.a.bi \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+2q^{7}+q^{11}-4q^{13}+4q^{17}+\cdots\)
7920.2.a.bj \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+2q^{7}+q^{11}+8q^{17}+8q^{19}+\cdots\)
7920.2.a.bk \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+2q^{7}+q^{11}+4q^{13}+4q^{19}+\cdots\)
7920.2.a.bl \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+4q^{7}-q^{11}-4q^{13}+6q^{17}+\cdots\)
7920.2.a.bm \(1\) \(63.242\) \(\Q\) None \(0\) \(0\) \(1\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+4q^{7}+q^{11}-4q^{13}+6q^{17}+\cdots\)
7920.2.a.bn \(2\) \(63.242\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}+(-1-\beta )q^{7}-q^{11}+(3-\beta )q^{13}+\cdots\)
7920.2.a.bo \(2\) \(63.242\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+(-1-\beta )q^{7}+q^{11}+(-1-\beta )q^{13}+\cdots\)
7920.2.a.bp \(2\) \(63.242\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+(-1+\beta )q^{7}+q^{11}+(1-\beta )q^{13}+\cdots\)
7920.2.a.bq \(2\) \(63.242\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-\beta q^{7}-q^{11}+2q^{13}+(2-\beta )q^{17}+\cdots\)
7920.2.a.br \(2\) \(63.242\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}+\beta q^{7}-q^{11}+(-2-\beta )q^{13}+\cdots\)
7920.2.a.bs \(2\) \(63.242\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}+\beta q^{7}-q^{11}+(2+\beta )q^{13}+(-2+\cdots)q^{17}+\cdots\)
7920.2.a.bt \(2\) \(63.242\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+\beta q^{7}+q^{11}+(2+\beta )q^{13}+(-2+\cdots)q^{17}+\cdots\)
7920.2.a.bu \(2\) \(63.242\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+\beta q^{7}+q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
7920.2.a.bv \(2\) \(63.242\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}+(1+\beta )q^{7}-q^{11}+(-1+3\beta )q^{13}+\cdots\)
7920.2.a.bw \(2\) \(63.242\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}+(2+\beta )q^{7}-q^{11}-\beta q^{13}+3\beta q^{17}+\cdots\)
7920.2.a.bx \(2\) \(63.242\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}+(2+\beta )q^{7}+q^{11}-\beta q^{13}-3\beta q^{17}+\cdots\)
7920.2.a.by \(2\) \(63.242\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-5\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}+(-2-\beta )q^{7}-q^{11}+(4-2\beta )q^{13}+\cdots\)
7920.2.a.bz \(2\) \(63.242\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-2q^{7}-q^{11}+(2+\beta )q^{13}+(-2+\cdots)q^{19}+\cdots\)
7920.2.a.ca \(2\) \(63.242\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-3\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+(-1-\beta )q^{7}+q^{11}+(2-2\beta )q^{13}+\cdots\)
7920.2.a.cb \(2\) \(63.242\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}+(-1+\beta )q^{7}-q^{11}+(1-\beta )q^{13}+\cdots\)
7920.2.a.cc \(2\) \(63.242\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}+\beta q^{7}+q^{11}+(-2-\beta )q^{13}+\cdots\)
7920.2.a.cd \(2\) \(63.242\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+(1+\beta )q^{7}+q^{11}+(-1+3\beta )q^{13}+\cdots\)
7920.2.a.ce \(2\) \(63.242\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+(1+\beta )q^{7}+q^{11}+(1-\beta )q^{13}+\cdots\)
7920.2.a.cf \(2\) \(63.242\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}+(2+\beta )q^{7}-q^{11}-\beta q^{13}+3\beta q^{17}+\cdots\)
7920.2.a.cg \(2\) \(63.242\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}+(2+\beta )q^{7}-q^{11}+2\beta q^{13}+\cdots\)
7920.2.a.ch \(2\) \(63.242\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(4\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+2q^{7}+q^{11}+(-4+\beta )q^{13}+\cdots\)
7920.2.a.ci \(2\) \(63.242\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(4\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}+(2+\beta )q^{7}+q^{11}-\beta q^{13}-3\beta q^{17}+\cdots\)
7920.2.a.cj \(3\) \(63.242\) 3.3.148.1 None \(0\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}-\beta _{2}q^{7}+q^{11}+(-1-\beta _{1})q^{13}+\cdots\)
7920.2.a.ck \(3\) \(63.242\) 3.3.1016.1 None \(0\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}-\beta _{2}q^{7}+q^{11}+(1-\beta _{1}-\beta _{2})q^{13}+\cdots\)
7920.2.a.cl \(3\) \(63.242\) 3.3.1016.1 None \(0\) \(0\) \(3\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}-\beta _{2}q^{7}-q^{11}+(1-\beta _{1}-\beta _{2})q^{13}+\cdots\)
7920.2.a.cm \(4\) \(63.242\) 4.4.48704.2 None \(0\) \(0\) \(-4\) \(-4\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}+(-1-\beta _{3})q^{7}-q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)
7920.2.a.cn \(4\) \(63.242\) 4.4.48704.2 None \(0\) \(0\) \(4\) \(-4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+(-1-\beta _{3})q^{7}+q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(660))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(880))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(990))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1584))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1980))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2640))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3960))\)\(^{\oplus 2}\)