Properties

Label 2415.2.cc
Level $2415$
Weight $2$
Character orbit 2415.cc
Rep. character $\chi_{2415}(76,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1280$
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.cc (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
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 1280 2640
Cusp forms 3760 1280 2480
Eisenstein series 160 0 160

Trace form

\( 1280q - 8q^{2} - 120q^{4} - 24q^{8} + 128q^{9} + O(q^{10}) \) \( 1280q - 8q^{2} - 120q^{4} - 24q^{8} + 128q^{9} - 192q^{16} + 8q^{18} + 8q^{23} - 128q^{25} + 24q^{29} - 48q^{32} - 32q^{35} + 164q^{36} + 88q^{43} + 44q^{44} - 32q^{46} + 4q^{49} + 36q^{50} + 88q^{51} - 220q^{56} + 188q^{58} - 72q^{64} + 72q^{71} + 24q^{72} - 44q^{74} - 24q^{77} - 16q^{78} + 88q^{79} - 128q^{81} + 8q^{85} - 660q^{88} + 800q^{92} - 32q^{95} - 80q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2415, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(805, [\chi])\)\(^{\oplus 2}\)