↑

Properties

Label 2415.2.cm
Level $2415$
Weight $2$
Character orbit 2415.cm
Rep. character $\chi_{2415}(16,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $2560$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2415.cm (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 7840 2560 5280
Cusp forms 7520 2560 4960
Eisenstein series 320 0 320

Trace form

\( 2560 q - 8 q^{2} + 120 q^{4} + 48 q^{8} + 128 q^{9} + O(q^{10}) \) \( 2560 q - 8 q^{2} + 120 q^{4} + 48 q^{8} + 128 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{14} + 192 q^{16} - 8 q^{18} + 8 q^{19} + 32 q^{22} - 8 q^{23} + 128 q^{25} + 48 q^{26} - 40 q^{28} + 56 q^{29} + 4 q^{31} + 72 q^{32} - 16 q^{33} - 32 q^{34} + 32 q^{35} - 328 q^{36} - 16 q^{37} + 360 q^{38} - 24 q^{40} - 32 q^{41} + 32 q^{42} - 112 q^{43} + 20 q^{44} + 8 q^{46} + 92 q^{49} - 72 q^{50} + 80 q^{51} - 32 q^{53} - 16 q^{55} + 228 q^{56} - 60 q^{58} + 76 q^{59} + 72 q^{61} - 144 q^{64} + 24 q^{65} - 32 q^{67} + 40 q^{68} - 24 q^{69} - 24 q^{71} - 24 q^{72} + 24 q^{73} + 36 q^{74} - 48 q^{76} - 24 q^{77} + 32 q^{78} - 52 q^{79} + 128 q^{81} + 232 q^{82} + 96 q^{83} - 48 q^{84} - 8 q^{85} - 128 q^{86} + 548 q^{88} - 32 q^{89} + 16 q^{90} - 40 q^{91} + 880 q^{92} - 412 q^{94} + 16 q^{95} + 32 q^{97} - 144 q^{98} + 16 q^{99} + O(q^{100}) \)

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

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