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Properties

Label 2415.2.cl
Level $2415$
Weight $2$
Character orbit 2415.cl
Rep. character $\chi_{2415}(41,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $2560$
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.cl (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
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 2560 1360
Cusp forms 3760 2560 1200
Eisenstein series 160 0 160

Trace form

\( 2560 q + 256 q^{4} + 8 q^{9} + O(q^{10}) \) \( 2560 q + 256 q^{4} + 8 q^{9} - 224 q^{16} - 32 q^{18} + 54 q^{21} + 32 q^{22} - 256 q^{25} - 8 q^{30} + 56 q^{36} - 32 q^{37} - 48 q^{39} - 48 q^{42} + 72 q^{43} + 16 q^{46} - 116 q^{49} - 40 q^{51} + 24 q^{57} - 16 q^{58} + 126 q^{63} + 192 q^{64} + 48 q^{67} - 24 q^{70} - 488 q^{72} + 304 q^{78} - 136 q^{79} - 8 q^{81} + 122 q^{84} - 128 q^{88} - 40 q^{91} - 56 q^{93} + 392 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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