↑

Properties

Label 2004.2.p
Level $2004$
Weight $2$
Character orbit 2004.p
Rep. character $\chi_{2004}(43,\cdot)$
Character field $\Q(\zeta_{166})$
Dimension $13776$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2004 = 2^{2} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2004.p (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 668 \)
Character field: \(\Q(\zeta_{166})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2004, [\chi])\).

Total New Old
Modular forms 27880 13776 14104
Cusp forms 27224 13776 13448
Eisenstein series 656 0 656

Trace form

\( 13776 q + 4 q^{4} - 4 q^{6} + 168 q^{9} + O(q^{10}) \) \( 13776 q + 4 q^{4} - 4 q^{6} + 168 q^{9} + 8 q^{12} + 16 q^{14} + 20 q^{16} + 28 q^{22} + 4 q^{24} + 168 q^{25} + 4 q^{28} - 4 q^{36} - 8 q^{38} - 20 q^{42} - 12 q^{44} - 16 q^{48} + 152 q^{49} - 48 q^{50} + 4 q^{54} + 36 q^{56} - 12 q^{58} + 48 q^{61} - 4 q^{62} + 28 q^{64} + 16 q^{65} + 8 q^{66} - 40 q^{76} - 16 q^{77} - 168 q^{81} + 40 q^{84} - 32 q^{85} - 80 q^{88} - 16 q^{89} + 32 q^{94} - 24 q^{96} + 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2004, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2004, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2004, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(668, [\chi])\)\(^{\oplus 2}\)