Properties

Label 4830.2.a
Level $4830$
Weight $2$
Character orbit 4830.a
Rep. character $\chi_{4830}(1,\cdot)$
Character field $\Q$
Dimension $87$
Newform subspaces $57$
Sturm bound $2304$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4830.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 57 \)
Sturm bound: \(2304\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4830))\).

Total New Old
Modular forms 1168 87 1081
Cusp forms 1137 87 1050
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.

\(2\)\(3\)\(5\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(36\)
Minus space\(-\)\(51\)

Trace form

\( 87q - q^{2} - q^{3} + 87q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + 87q^{9} + O(q^{10}) \) \( 87q - q^{2} - q^{3} + 87q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + 87q^{9} - q^{10} - 12q^{11} - q^{12} - 14q^{13} - q^{14} - q^{15} + 87q^{16} - 18q^{17} - q^{18} - 20q^{19} - q^{20} - q^{21} - 12q^{22} - q^{23} - q^{24} + 87q^{25} - 14q^{26} - q^{27} - q^{28} - 30q^{29} - q^{30} - q^{32} + 20q^{33} - 18q^{34} - q^{35} + 87q^{36} - 6q^{37} - 20q^{38} - 14q^{39} - q^{40} - 10q^{41} - q^{42} + 20q^{43} - 12q^{44} - q^{45} - q^{46} - 16q^{47} - q^{48} + 87q^{49} - q^{50} + 14q^{51} - 14q^{52} - 22q^{53} - q^{54} - 12q^{55} - q^{56} - 20q^{57} - 14q^{58} - 28q^{59} - q^{60} + 2q^{61} - q^{63} + 87q^{64} - 14q^{65} - 12q^{66} - 36q^{67} - 18q^{68} - q^{69} + 7q^{70} - 24q^{71} - q^{72} - 42q^{73} + 10q^{74} - q^{75} - 20q^{76} - 12q^{77} + 2q^{78} - 32q^{79} - q^{80} + 87q^{81} - 10q^{82} - 20q^{83} - q^{84} - 2q^{85} + 4q^{86} + 34q^{87} - 12q^{88} - 58q^{89} - q^{90} - 14q^{91} - q^{92} - 16q^{93} + 80q^{94} - 4q^{95} - q^{96} - 34q^{97} - q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4830))\) 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 7 23
4830.2.a.a \(1\) \(38.568\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.b \(1\) \(38.568\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.c \(1\) \(38.568\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.d \(1\) \(38.568\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.e \(1\) \(38.568\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.f \(1\) \(38.568\) \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.g \(1\) \(38.568\) \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.h \(1\) \(38.568\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.i \(1\) \(38.568\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.j \(1\) \(38.568\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.k \(1\) \(38.568\) \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.l \(1\) \(38.568\) \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.m \(1\) \(38.568\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.n \(1\) \(38.568\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.o \(1\) \(38.568\) \(\Q\) None \(-1\) \(1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.p \(1\) \(38.568\) \(\Q\) None \(-1\) \(1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.q \(1\) \(38.568\) \(\Q\) None \(-1\) \(1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.r \(1\) \(38.568\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.s \(1\) \(38.568\) \(\Q\) None \(1\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.t \(1\) \(38.568\) \(\Q\) None \(1\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.u \(1\) \(38.568\) \(\Q\) None \(1\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.v \(1\) \(38.568\) \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.w \(1\) \(38.568\) \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.x \(1\) \(38.568\) \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.y \(1\) \(38.568\) \(\Q\) None \(1\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.z \(1\) \(38.568\) \(\Q\) None \(1\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.ba \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bb \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bc \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bd \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.be \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bf \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bg \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bh \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bi \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bj \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bk \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bl \(1\) \(38.568\) \(\Q\) None \(1\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bm \(2\) \(38.568\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bn \(2\) \(38.568\) \(\Q(\sqrt{13}) \) None \(-2\) \(2\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.bo \(2\) \(38.568\) \(\Q(\sqrt{13}) \) None \(-2\) \(2\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.bp \(2\) \(38.568\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.bq \(2\) \(38.568\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.br \(2\) \(38.568\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.bs \(2\) \(38.568\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.bt \(2\) \(38.568\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.bu \(2\) \(38.568\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.bv \(2\) \(38.568\) \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bw \(3\) \(38.568\) 3.3.316.1 None \(-3\) \(-3\) \(-3\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bx \(3\) \(38.568\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(3\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.by \(3\) \(38.568\) 3.3.148.1 None \(-3\) \(-3\) \(3\) \(3\) \(+\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bz \(3\) \(38.568\) 3.3.148.1 None \(3\) \(-3\) \(-3\) \(3\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.ca \(3\) \(38.568\) 3.3.316.1 None \(3\) \(-3\) \(3\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.cb \(3\) \(38.568\) 3.3.229.1 None \(3\) \(-3\) \(3\) \(3\) \(-\) \(+\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.cc \(3\) \(38.568\) \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(-3\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.cd \(4\) \(38.568\) 4.4.10273.1 None \(-4\) \(-4\) \(-4\) \(4\) \(+\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.ce \(4\) \(38.568\) 4.4.6809.1 None \(4\) \(4\) \(4\) \(4\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4830))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4830)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(805))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1610))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2415))\)\(^{\oplus 2}\)