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

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

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

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