Properties

Label 120.2.v
Level $120$
Weight $2$
Character orbit 120.v
Rep. character $\chi_{120}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 56 24 32
Cusp forms 40 24 16
Eisenstein series 16 0 16

Trace form

\( 24q + 4q^{6} - 12q^{8} + O(q^{10}) \) \( 24q + 4q^{6} - 12q^{8} + 8q^{10} - 8q^{12} - 20q^{16} + 8q^{17} - 20q^{20} - 28q^{22} - 8q^{25} - 16q^{26} + 4q^{28} + 8q^{30} + 20q^{32} - 48q^{35} + 4q^{36} + 40q^{38} + 8q^{40} + 20q^{42} - 32q^{43} + 48q^{46} + 16q^{48} + 56q^{50} - 16q^{51} - 48q^{52} - 32q^{56} - 12q^{58} + 20q^{60} - 16q^{62} - 8q^{65} - 24q^{66} + 48q^{67} + 72q^{68} + 4q^{70} + 12q^{72} - 40q^{73} + 48q^{76} - 24q^{78} + 76q^{80} - 24q^{81} + 24q^{82} + 80q^{83} - 32q^{86} + 12q^{88} - 12q^{90} + 64q^{91} + 16q^{92} - 44q^{96} - 24q^{97} - 88q^{98} + O(q^{100}) \)

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.v.a \(24\) \(0.958\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)