↑

Properties

Label 2015.2.q
Level $2015$
Weight $2$
Character orbit 2015.q
Rep. character $\chi_{2015}(92,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $384$
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.q (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(i)\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 456 384 72
Cusp forms 440 384 56
Eisenstein series 16 0 16

Trace form

\( 384 q + 16 q^{7} - 12 q^{8} + O(q^{10}) \) \( 384 q + 16 q^{7} - 12 q^{8} - 16 q^{10} - 368 q^{16} - 32 q^{20} - 56 q^{25} - 36 q^{28} - 8 q^{31} + 56 q^{32} + 56 q^{33} - 320 q^{36} + 36 q^{38} - 24 q^{40} + 16 q^{41} - 24 q^{45} - 40 q^{47} + 112 q^{50} + 32 q^{51} + 112 q^{56} - 32 q^{62} - 64 q^{63} - 144 q^{66} + 48 q^{67} + 76 q^{70} - 96 q^{71} - 100 q^{72} - 16 q^{76} + 96 q^{80} - 272 q^{81} - 92 q^{82} + 96 q^{87} + 164 q^{90} + 124 q^{93} - 56 q^{95} + 136 q^{97} - 28 q^{98} + O(q^{100}) \)

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

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