Properties

Label 4650.2.a
Level $4650$
Weight $2$
Character orbit 4650.a
Rep. character $\chi_{4650}(1,\cdot)$
Character field $\Q$
Dimension $94$
Newform subspaces $68$
Sturm bound $1920$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4650.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 68 \)
Sturm bound: \(1920\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4650))\).

Total New Old
Modular forms 984 94 890
Cusp forms 937 94 843
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.

\(2\)\(3\)\(5\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(38\)
Minus space\(-\)\(56\)

Trace form

\( 94q - 2q^{2} + 94q^{4} - 8q^{7} - 2q^{8} + 94q^{9} + O(q^{10}) \) \( 94q - 2q^{2} + 94q^{4} - 8q^{7} - 2q^{8} + 94q^{9} - 16q^{11} - 12q^{13} - 8q^{14} + 94q^{16} - 4q^{17} - 2q^{18} - 12q^{19} + 20q^{26} - 8q^{28} + 36q^{29} - 2q^{32} - 4q^{33} + 36q^{34} + 94q^{36} + 12q^{37} + 28q^{41} + 8q^{42} - 8q^{43} - 16q^{44} - 8q^{46} + 24q^{47} + 78q^{49} - 20q^{51} - 12q^{52} - 20q^{53} - 8q^{56} - 16q^{57} - 12q^{58} - 24q^{59} - 20q^{61} - 8q^{63} + 94q^{64} - 8q^{66} - 12q^{67} - 4q^{68} - 16q^{69} + 8q^{71} - 2q^{72} - 12q^{73} - 12q^{74} - 12q^{76} + 48q^{77} - 12q^{78} - 8q^{79} + 94q^{81} + 4q^{82} + 48q^{83} + 8q^{87} + 20q^{89} - 40q^{91} + 2q^{93} - 28q^{94} + 16q^{97} - 18q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4650))\) 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 31
4650.2.a.a \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-5\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-5q^{7}-q^{8}+\cdots\)
4650.2.a.b \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
4650.2.a.c \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.d \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.e \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.f \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.g \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.h \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
4650.2.a.i \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.j \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.k \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.l \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots\)
4650.2.a.m \(1\) \(37.130\) \(\Q\) None \(-1\) \(-1\) \(0\) \(5\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots\)
4650.2.a.n \(1\) \(37.130\) \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
4650.2.a.o \(1\) \(37.130\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.p \(1\) \(37.130\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.q \(1\) \(37.130\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.r \(1\) \(37.130\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
4650.2.a.s \(1\) \(37.130\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
4650.2.a.t \(1\) \(37.130\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.u \(1\) \(37.130\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.v \(1\) \(37.130\) \(\Q\) None \(-1\) \(1\) \(0\) \(3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots\)
4650.2.a.w \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
4650.2.a.x \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
4650.2.a.y \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.z \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.ba \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
4650.2.a.bb \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
4650.2.a.bc \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bd \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.be \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bf \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bg \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bh \(1\) \(37.130\) \(\Q\) None \(1\) \(-1\) \(0\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bi \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(-5\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-5q^{7}+q^{8}+\cdots\)
4650.2.a.bj \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(-3\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.bk \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.bl \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bm \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bn \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bo \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bp \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
4650.2.a.bq \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.br \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bs \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bt \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bu \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
4650.2.a.bv \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
4650.2.a.bw \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
4650.2.a.bx \(1\) \(37.130\) \(\Q\) None \(1\) \(1\) \(0\) \(5\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+5q^{7}+q^{8}+\cdots\)
4650.2.a.by \(2\) \(37.130\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-\beta q^{7}-q^{8}+\cdots\)
4650.2.a.bz \(2\) \(37.130\) \(\Q(\sqrt{65}) \) None \(-2\) \(-2\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots\)
4650.2.a.ca \(2\) \(37.130\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(0\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(2+\beta )q^{7}+\cdots\)
4650.2.a.cb \(2\) \(37.130\) \(\Q(\sqrt{13}) \) None \(-2\) \(-2\) \(0\) \(6\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots\)
4650.2.a.cc \(2\) \(37.130\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-2+\beta )q^{7}+\cdots\)
4650.2.a.cd \(2\) \(37.130\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-2\beta q^{7}-q^{8}+\cdots\)
4650.2.a.ce \(2\) \(37.130\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-\beta q^{7}-q^{8}+\cdots\)
4650.2.a.cf \(2\) \(37.130\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(2+\beta )q^{7}+\cdots\)
4650.2.a.cg \(2\) \(37.130\) \(\Q(\sqrt{13}) \) None \(2\) \(2\) \(0\) \(-6\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.ch \(2\) \(37.130\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+(-2-\beta )q^{7}+\cdots\)
4650.2.a.ci \(3\) \(37.130\) 3.3.1708.1 None \(-3\) \(-3\) \(0\) \(-6\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.cj \(3\) \(37.130\) 3.3.837.1 None \(-3\) \(3\) \(0\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-\beta _{2}q^{7}-q^{8}+\cdots\)
4650.2.a.ck \(3\) \(37.130\) 3.3.940.1 None \(-3\) \(3\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
4650.2.a.cl \(3\) \(37.130\) 3.3.1373.1 None \(-3\) \(3\) \(0\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(1-\beta _{2})q^{7}+\cdots\)
4650.2.a.cm \(3\) \(37.130\) 3.3.1373.1 None \(3\) \(-3\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-1+\beta _{2})q^{7}+\cdots\)
4650.2.a.cn \(3\) \(37.130\) 3.3.940.1 None \(3\) \(-3\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
4650.2.a.co \(3\) \(37.130\) 3.3.837.1 None \(3\) \(-3\) \(0\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+\beta _{2}q^{7}+q^{8}+\cdots\)
4650.2.a.cp \(3\) \(37.130\) 3.3.1708.1 None \(3\) \(3\) \(0\) \(6\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4650))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4650)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(775))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(930))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2325))\)\(^{\oplus 2}\)