↑

Properties

Label 3381.2.w
Level $3381$
Weight $2$
Character orbit 3381.w
Rep. character $\chi_{3381}(461,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $2472$
Sturm bound $896$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3381.w (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3381, [\chi])\).

Total New Old
Modular forms 2712 2472 240
Cusp forms 2664 2472 192
Eisenstein series 48 0 48

Trace form

\( 2472 q + 416 q^{4} + 4 q^{7} + O(q^{10}) \) \( 2472 q + 416 q^{4} + 4 q^{7} + 70 q^{12} + 12 q^{15} - 424 q^{16} + 20 q^{18} - 6 q^{21} - 44 q^{22} - 396 q^{25} - 88 q^{28} + 24 q^{30} - 80 q^{37} + 20 q^{39} - 84 q^{40} - 96 q^{42} + 48 q^{43} - 42 q^{45} - 36 q^{49} + 16 q^{51} - 252 q^{52} + 196 q^{55} - 2 q^{57} + 140 q^{58} - 188 q^{60} - 196 q^{61} + 22 q^{63} + 416 q^{64} - 196 q^{66} - 48 q^{67} + 12 q^{70} - 84 q^{72} - 252 q^{75} - 336 q^{76} + 44 q^{78} + 16 q^{81} - 332 q^{84} - 40 q^{85} - 112 q^{87} + 24 q^{88} - 350 q^{90} - 148 q^{91} + 252 q^{96} - 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3381, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3381, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)