Properties

Label 2415.2.cg
Level $2415$
Weight $2$
Character orbit 2415.cg
Rep. character $\chi_{2415}(64,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1440$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2415.cg (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2415, [\chi])\).

Total New Old
Modular forms 3920 1440 2480
Cusp forms 3760 1440 2320
Eisenstein series 160 0 160

Trace form

\( 1440q + 136q^{4} + 8q^{6} + 144q^{9} + O(q^{10}) \) \( 1440q + 136q^{4} + 8q^{6} + 144q^{9} - 8q^{15} - 120q^{16} + 40q^{20} - 8q^{21} - 24q^{24} + 36q^{25} - 80q^{26} + 16q^{29} + 8q^{30} + 32q^{31} + 12q^{34} - 8q^{35} - 136q^{36} + 72q^{39} + 40q^{40} + 216q^{44} + 32q^{46} + 144q^{49} + 56q^{50} - 16q^{51} + 36q^{54} + 84q^{55} + 48q^{56} - 16q^{59} + 32q^{60} + 48q^{61} + 216q^{64} - 8q^{65} + 16q^{66} - 8q^{69} + 8q^{70} - 16q^{71} - 112q^{74} - 16q^{75} + 232q^{76} + 80q^{79} - 144q^{81} + 24q^{84} + 4q^{85} + 832q^{86} - 16q^{89} + 320q^{91} - 176q^{94} - 192q^{95} + 48q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2415, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2415, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2415, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(805, [\chi])\)\(^{\oplus 2}\)