Properties

Label 240.2.bl
Level $240$
Weight $2$
Character orbit 240.bl
Rep. character $\chi_{240}(109,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.bl (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(240, [\chi])\).

Total New Old
Modular forms 104 48 56
Cusp forms 88 48 40
Eisenstein series 16 0 16

Trace form

\( 48q + O(q^{10}) \) \( 48q + 12q^{10} - 16q^{14} - 4q^{16} + 8q^{19} - 4q^{24} - 40q^{26} - 8q^{30} - 48q^{31} - 28q^{34} + 24q^{35} - 4q^{36} - 16q^{40} - 40q^{44} - 4q^{46} + 48q^{49} - 32q^{50} + 8q^{51} - 4q^{54} + 48q^{56} - 32q^{59} - 24q^{60} + 16q^{61} + 48q^{64} + 16q^{65} + 24q^{66} - 16q^{69} + 40q^{74} - 16q^{75} + 60q^{76} - 96q^{79} + 72q^{80} - 48q^{81} + 16q^{86} + 8q^{90} - 32q^{91} + 44q^{94} - 48q^{95} - 40q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
240.2.bl.a \(48\) \(1.916\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)