↑

Properties

Label 3009.2.bh
Level $3009$
Weight $2$
Character orbit 3009.bh
Rep. character $\chi_{3009}(2,\cdot)$
Character field $\Q(\zeta_{232})$
Dimension $39872$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3009.bh (of order \(232\) and degree \(112\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3009 \)
Character field: \(\Q(\zeta_{232})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3009, [\chi])\).

Total New Old
Modular forms 40768 40768 0
Cusp forms 39872 39872 0
Eisenstein series 896 896 0

Trace form

\( 39872 q - 108 q^{3} - 116 q^{6} - 216 q^{7} - 132 q^{9} + O(q^{10}) \) \( 39872 q - 108 q^{3} - 116 q^{6} - 216 q^{7} - 132 q^{9} - 232 q^{10} - 108 q^{12} - 120 q^{15} + 944 q^{16} - 232 q^{18} - 216 q^{19} - 216 q^{22} - 116 q^{24} - 216 q^{25} - 108 q^{27} - 280 q^{28} - 232 q^{31} - 232 q^{33} - 232 q^{34} - 180 q^{36} - 232 q^{37} - 116 q^{39} - 232 q^{40} - 116 q^{42} - 232 q^{43} - 128 q^{45} - 184 q^{46} + 68 q^{48} - 248 q^{49} - 28 q^{51} - 464 q^{52} + 696 q^{54} - 100 q^{57} - 1512 q^{60} - 232 q^{61} - 84 q^{63} - 100 q^{66} - 464 q^{67} - 232 q^{69} - 232 q^{70} - 232 q^{73} - 100 q^{75} - 248 q^{76} - 20 q^{78} - 216 q^{79} - 232 q^{82} - 360 q^{84} - 264 q^{85} - 116 q^{87} - 200 q^{88} - 116 q^{90} - 232 q^{91} - 116 q^{93} - 376 q^{94} - 116 q^{96} - 232 q^{97} - 116 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3009, [\chi])\) into newform subspaces

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