Properties

Label 120.2.b
Level $120$
Weight $2$
Character orbit 120.b
Rep. character $\chi_{120}(11,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $48$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(120, [\chi])\).

Total New Old
Modular forms 28 16 12
Cusp forms 20 16 4
Eisenstein series 8 0 8

Trace form

\( 16q + 2q^{4} - 6q^{6} + O(q^{10}) \) \( 16q + 2q^{4} - 6q^{6} - 2q^{10} - 16q^{12} - 14q^{16} + 4q^{18} - 8q^{19} + 28q^{22} - 2q^{24} + 16q^{25} - 24q^{27} - 4q^{28} - 8q^{30} - 8q^{33} - 6q^{36} - 14q^{40} + 32q^{42} - 16q^{46} - 4q^{48} - 32q^{49} + 40q^{51} + 40q^{52} + 26q^{54} - 8q^{57} - 4q^{58} - 14q^{60} + 50q^{64} - 16q^{66} - 64q^{67} + 12q^{70} + 32q^{72} - 16q^{73} - 24q^{76} + 24q^{78} + 16q^{81} - 8q^{82} + 56q^{84} + 28q^{88} + 18q^{90} + 48q^{91} - 80q^{94} - 26q^{96} + 16q^{97} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(120, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
120.2.b.a \(8\) \(0.958\) 8.0.1649659456.5 None \(-1\) \(0\) \(8\) \(0\) \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
120.2.b.b \(8\) \(0.958\) 8.0.1649659456.5 None \(1\) \(0\) \(-8\) \(0\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)