Properties

Label 2415.2.dk
Level $2415$
Weight $2$
Character orbit 2415.dk
Rep. character $\chi_{2415}(2,\cdot)$
Character field $\Q(\zeta_{132})$
Dimension $15040$
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.dk (of order \(132\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2415 \)
Character field: \(\Q(\zeta_{132})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 15680 15680 0
Cusp forms 15040 15040 0
Eisenstein series 640 640 0

Trace form

\( 15040 q - 18 q^{3} - 128 q^{6} - 72 q^{7} + O(q^{10}) \) \( 15040 q - 18 q^{3} - 128 q^{6} - 72 q^{7} - 36 q^{10} - 2 q^{12} - 144 q^{13} - 72 q^{15} - 776 q^{16} + 38 q^{18} - 32 q^{21} - 320 q^{22} - 52 q^{25} - 72 q^{27} + 8 q^{28} - 38 q^{30} - 72 q^{31} + 6 q^{33} - 128 q^{36} + 36 q^{37} - 12 q^{40} + 8 q^{42} - 208 q^{43} - 80 q^{45} - 56 q^{46} - 88 q^{48} - 36 q^{51} + 324 q^{52} - 64 q^{55} + 48 q^{57} - 52 q^{58} + 38 q^{60} - 264 q^{61} - 64 q^{63} - 84 q^{66} - 68 q^{67} - 272 q^{70} + 86 q^{72} - 84 q^{73} - 2 q^{75} - 160 q^{76} - 92 q^{81} - 60 q^{82} - 128 q^{85} + 26 q^{87} + 60 q^{88} - 352 q^{91} + 12 q^{93} - 220 q^{96} - 48 q^{97} + O(q^{100}) \)

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

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