Properties

Label 5550.2.a
Level $5550$
Weight $2$
Character orbit 5550.a
Rep. character $\chi_{5550}(1,\cdot)$
Character field $\Q$
Dimension $114$
Newform subspaces $68$
Sturm bound $2280$
Trace bound $17$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5550.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 68 \)
Sturm bound: \(2280\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5550))\).

Total New Old
Modular forms 1164 114 1050
Cusp forms 1117 114 1003
Eisenstein series 47 0 47

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

\(2\)\(3\)\(5\)\(37\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(42\)
Minus space\(-\)\(72\)

Trace form

\( 114q + 114q^{4} - 2q^{6} - 12q^{7} + 114q^{9} + O(q^{10}) \) \( 114q + 114q^{4} - 2q^{6} - 12q^{7} + 114q^{9} + 4q^{13} + 8q^{14} + 114q^{16} + 8q^{17} - 12q^{19} + 8q^{22} - 8q^{23} - 2q^{24} + 8q^{26} - 12q^{28} - 8q^{29} + 12q^{31} - 12q^{33} + 114q^{36} + 2q^{37} + 20q^{38} + 20q^{41} - 12q^{43} + 12q^{46} + 32q^{47} + 126q^{49} + 4q^{51} + 4q^{52} + 28q^{53} - 2q^{54} + 8q^{56} + 4q^{57} + 20q^{58} + 8q^{59} - 12q^{61} - 12q^{62} - 12q^{63} + 114q^{64} + 8q^{68} - 8q^{69} + 8q^{71} - 12q^{76} - 8q^{78} - 36q^{79} + 114q^{81} + 24q^{83} + 4q^{86} - 28q^{87} + 8q^{88} - 48q^{89} - 32q^{91} - 8q^{92} - 4q^{93} - 16q^{94} - 2q^{96} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5550))\) 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 37
5550.2.a.a \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
5550.2.a.b \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
5550.2.a.c \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
5550.2.a.d \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
5550.2.a.e \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
5550.2.a.f \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
5550.2.a.g \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
5550.2.a.h \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
5550.2.a.i \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
5550.2.a.j \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
5550.2.a.k \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(5\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots\)
5550.2.a.l \(1\) \(44.317\) \(\Q\) None \(-1\) \(-1\) \(0\) \(5\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots\)
5550.2.a.m \(1\) \(44.317\) \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
5550.2.a.n \(1\) \(44.317\) \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
5550.2.a.o \(1\) \(44.317\) \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
5550.2.a.p \(1\) \(44.317\) \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
5550.2.a.q \(1\) \(44.317\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5550.2.a.r \(1\) \(44.317\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5550.2.a.s \(1\) \(44.317\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
5550.2.a.t \(1\) \(44.317\) \(\Q\) None \(-1\) \(1\) \(0\) \(3\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots\)
5550.2.a.u \(1\) \(44.317\) \(\Q\) None \(-1\) \(1\) \(0\) \(4\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
5550.2.a.v \(1\) \(44.317\) \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
5550.2.a.w \(1\) \(44.317\) \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
5550.2.a.x \(1\) \(44.317\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
5550.2.a.y \(1\) \(44.317\) \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
5550.2.a.z \(1\) \(44.317\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
5550.2.a.ba \(1\) \(44.317\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
5550.2.a.bb \(1\) \(44.317\) \(\Q\) None \(1\) \(-1\) \(0\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
5550.2.a.bc \(1\) \(44.317\) \(\Q\) None \(1\) \(-1\) \(0\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
5550.2.a.bd \(1\) \(44.317\) \(\Q\) None \(1\) \(-1\) \(0\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots\)
5550.2.a.be \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(-5\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-5q^{7}+q^{8}+\cdots\)
5550.2.a.bf \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
5550.2.a.bg \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
5550.2.a.bh \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
5550.2.a.bi \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
5550.2.a.bj \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
5550.2.a.bk \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
5550.2.a.bl \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
5550.2.a.bm \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
5550.2.a.bn \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
5550.2.a.bo \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
5550.2.a.bp \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
5550.2.a.bq \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
5550.2.a.br \(1\) \(44.317\) \(\Q\) None \(1\) \(1\) \(0\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
5550.2.a.bs \(2\) \(44.317\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-1+\beta )q^{7}+\cdots\)
5550.2.a.bt \(2\) \(44.317\) \(\Q(\sqrt{6}) \) None \(-2\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-1+\beta )q^{7}+\cdots\)
5550.2.a.bu \(2\) \(44.317\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
5550.2.a.bv \(2\) \(44.317\) \(\Q(\sqrt{33}) \) None \(-2\) \(2\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5550.2.a.bw \(2\) \(44.317\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(0\) \(2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
5550.2.a.bx \(2\) \(44.317\) \(\Q(\sqrt{113}) \) None \(2\) \(-2\) \(0\) \(-6\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-3q^{7}+q^{8}+\cdots\)
5550.2.a.by \(2\) \(44.317\) \(\Q(\sqrt{33}) \) None \(2\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
5550.2.a.bz \(2\) \(44.317\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(0\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
5550.2.a.ca \(2\) \(44.317\) \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta q^{7}+q^{8}+\cdots\)
5550.2.a.cb \(2\) \(44.317\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots\)
5550.2.a.cc \(2\) \(44.317\) \(\Q(\sqrt{6}) \) None \(2\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots\)
5550.2.a.cd \(3\) \(44.317\) 3.3.993.1 None \(-3\) \(-3\) \(0\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
5550.2.a.ce \(3\) \(44.317\) 3.3.257.1 None \(-3\) \(3\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
5550.2.a.cf \(3\) \(44.317\) 3.3.568.1 None \(-3\) \(3\) \(0\) \(3\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
5550.2.a.cg \(3\) \(44.317\) 3.3.568.1 None \(3\) \(-3\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
5550.2.a.ch \(3\) \(44.317\) 3.3.257.1 None \(3\) \(-3\) \(0\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
5550.2.a.ci \(3\) \(44.317\) 3.3.993.1 None \(3\) \(3\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
5550.2.a.cj \(4\) \(44.317\) 4.4.54764.1 None \(-4\) \(-4\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
5550.2.a.ck \(4\) \(44.317\) 4.4.358377.1 None \(-4\) \(4\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
5550.2.a.cl \(4\) \(44.317\) 4.4.30056.1 None \(-4\) \(4\) \(0\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
5550.2.a.cm \(4\) \(44.317\) 4.4.30056.1 None \(4\) \(-4\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
5550.2.a.cn \(4\) \(44.317\) 4.4.358377.1 None \(4\) \(-4\) \(0\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
5550.2.a.co \(5\) \(44.317\) 5.5.60594425.1 None \(-5\) \(-5\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-\beta _{4}q^{7}-q^{8}+\cdots\)
5550.2.a.cp \(5\) \(44.317\) 5.5.60594425.1 None \(5\) \(5\) \(0\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta _{4}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5550))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(555))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(925))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2775))\)\(^{\oplus 2}\)