↑

Properties

Label 3009.2.j
Level $3009$
Weight $2$
Character orbit 3009.j
Rep. character $\chi_{3009}(1594,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $344$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 728 344 384
Cusp forms 712 344 368
Eisenstein series 16 0 16

Trace form

\( 344 q - 336 q^{4} + 8 q^{5} - 8 q^{6} + 8 q^{7} + O(q^{10}) \) \( 344 q - 336 q^{4} + 8 q^{5} - 8 q^{6} + 8 q^{7} - 8 q^{11} + 8 q^{13} + 336 q^{16} + 32 q^{17} + 8 q^{18} - 8 q^{20} + 16 q^{21} - 8 q^{22} + 32 q^{23} + 32 q^{24} - 56 q^{28} - 32 q^{29} + 8 q^{31} - 8 q^{33} - 8 q^{34} + 16 q^{35} + 8 q^{37} - 80 q^{38} + 16 q^{40} - 48 q^{41} + 72 q^{44} - 8 q^{45} - 32 q^{46} + 40 q^{50} + 8 q^{51} + 16 q^{52} - 8 q^{54} - 24 q^{55} - 56 q^{56} + 16 q^{57} + 96 q^{58} - 16 q^{61} - 96 q^{62} + 8 q^{63} - 272 q^{64} - 32 q^{67} - 160 q^{68} + 56 q^{69} - 24 q^{72} - 64 q^{73} + 72 q^{74} + 32 q^{75} - 24 q^{78} + 40 q^{79} - 80 q^{80} - 344 q^{81} + 24 q^{82} - 96 q^{84} + 8 q^{85} + 80 q^{86} - 48 q^{88} - 16 q^{89} - 16 q^{91} - 80 q^{92} - 16 q^{95} - 16 q^{96} + 56 q^{97} - 72 q^{98} - 8 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3009, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1003, [\chi])\)\(^{\oplus 2}\)