↑

Properties

Label 2004.2.o
Level $2004$
Weight $2$
Character orbit 2004.o
Rep. character $\chi_{2004}(11,\cdot)$
Character field $\Q(\zeta_{166})$
Dimension $27224$
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.o (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2004 \)
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 27880 0
Cusp forms 27224 27224 0
Eisenstein series 656 656 0

Trace form

\( 27224 q - 166 q^{4} - 83 q^{6} - 162 q^{9} + O(q^{10}) \) \( 27224 q - 166 q^{4} - 83 q^{6} - 162 q^{9} - 166 q^{10} - 93 q^{12} - 324 q^{13} - 150 q^{16} - 93 q^{18} - 166 q^{21} - 162 q^{22} - 73 q^{24} - 8 q^{25} - 194 q^{28} - 83 q^{30} - 150 q^{33} - 154 q^{34} - 83 q^{36} - 324 q^{37} - 166 q^{40} - 62 q^{42} - 190 q^{45} - 198 q^{46} - 98 q^{48} - 16 q^{49} - 170 q^{52} - 82 q^{54} - 174 q^{57} - 190 q^{58} - 59 q^{60} - 356 q^{61} - 154 q^{64} - 115 q^{66} - 142 q^{69} - 166 q^{70} - 38 q^{72} - 324 q^{73} - 222 q^{76} - 45 q^{78} - 202 q^{81} - 118 q^{82} - 110 q^{84} - 332 q^{85} - 142 q^{88} - 63 q^{90} - 142 q^{93} - 178 q^{94} - 97 q^{96} - 324 q^{97} + O(q^{100}) \)

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.