↑

Properties

Label 2015.2.gg
Level $2015$
Weight $2$
Character orbit 2015.gg
Rep. character $\chi_{2015}(46,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2368$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.gg (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2015, [\chi])\).

Total New Old
Modular forms 3648 2368 1280
Cusp forms 3520 2368 1152
Eisenstein series 128 0 128

Trace form

\( 2368 q - 16 q^{7} + 36 q^{8} - 288 q^{9} + O(q^{10}) \) \( 2368 q - 16 q^{7} + 36 q^{8} - 288 q^{9} - 40 q^{11} + 20 q^{13} + 80 q^{14} - 272 q^{16} - 80 q^{18} - 8 q^{19} - 32 q^{20} + 60 q^{21} + 72 q^{28} - 88 q^{31} + 256 q^{32} + 64 q^{33} + 72 q^{36} - 16 q^{39} + 28 q^{41} + 180 q^{43} + 40 q^{44} + 8 q^{45} + 80 q^{46} - 48 q^{47} + 168 q^{49} + 100 q^{52} - 180 q^{58} - 88 q^{59} + 24 q^{62} + 88 q^{63} - 96 q^{66} - 40 q^{67} - 216 q^{69} - 16 q^{70} + 328 q^{72} - 232 q^{76} - 188 q^{78} - 80 q^{79} + 96 q^{80} + 200 q^{81} + 240 q^{82} - 240 q^{84} - 120 q^{86} + 80 q^{87} - 20 q^{89} - 220 q^{91} + 268 q^{93} + 16 q^{94} + 40 q^{96} + 28 q^{97} - 336 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2015, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2015, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2015, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)