↑

Properties

Label 2015.2.er
Level $2015$
Weight $2$
Character orbit 2015.er
Rep. character $\chi_{2015}(151,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1216$
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.er (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 1824 1216 608
Cusp forms 1760 1216 544
Eisenstein series 64 0 64

Trace form

\( 1216 q + 24 q^{7} - 36 q^{8} + 320 q^{9} + O(q^{10}) \) \( 1216 q + 24 q^{7} - 36 q^{8} + 320 q^{9} - 20 q^{11} - 20 q^{13} - 8 q^{14} + 352 q^{16} + 8 q^{18} - 24 q^{19} - 16 q^{20} - 80 q^{21} - 120 q^{28} - 4 q^{31} - 112 q^{32} + 32 q^{33} + 40 q^{39} - 4 q^{41} - 40 q^{44} - 8 q^{45} + 40 q^{46} - 48 q^{47} - 100 q^{52} + 180 q^{58} - 56 q^{59} - 216 q^{63} + 192 q^{66} - 88 q^{67} + 16 q^{70} - 96 q^{71} - 16 q^{72} - 200 q^{76} + 44 q^{78} + 80 q^{79} + 48 q^{80} - 592 q^{81} + 240 q^{84} + 120 q^{86} + 160 q^{87} + 20 q^{89} - 280 q^{91} - 72 q^{93} - 16 q^{94} - 40 q^{96} + 164 q^{97} + 24 q^{98} + O(q^{100}) \)

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

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