↑

Properties

Label 3381.2.q
Level $3381$
Weight $2$
Character orbit 3381.q
Rep. character $\chi_{3381}(484,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $1224$
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.q (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 2712 1224 1488
Cusp forms 2664 1224 1440
Eisenstein series 48 0 48

Trace form

\( 1224 q + 4 q^{3} - 200 q^{4} + 4 q^{6} + 8 q^{7} + 24 q^{8} - 204 q^{9} + O(q^{10}) \) \( 1224 q + 4 q^{3} - 200 q^{4} + 4 q^{6} + 8 q^{7} + 24 q^{8} - 204 q^{9} + 32 q^{10} + 12 q^{12} + 24 q^{13} + 36 q^{14} - 20 q^{15} - 160 q^{16} + 16 q^{17} + 16 q^{19} + 56 q^{20} + 12 q^{21} + 20 q^{22} - 48 q^{24} - 172 q^{25} + 32 q^{26} + 4 q^{27} - 36 q^{28} + 24 q^{29} - 112 q^{31} - 120 q^{32} + 24 q^{33} - 56 q^{34} + 40 q^{35} - 200 q^{36} - 36 q^{37} - 16 q^{38} - 60 q^{39} - 12 q^{40} + 4 q^{41} + 16 q^{42} + 16 q^{43} - 80 q^{44} - 52 q^{47} - 168 q^{48} + 52 q^{49} + 24 q^{50} - 52 q^{52} + 8 q^{53} + 4 q^{54} - 40 q^{55} + 124 q^{56} + 40 q^{57} + 36 q^{58} + 60 q^{59} - 60 q^{60} - 12 q^{61} + 16 q^{62} - 20 q^{63} - 240 q^{64} + 24 q^{65} + 48 q^{66} + 80 q^{67} + 192 q^{68} + 8 q^{69} + 84 q^{70} - 152 q^{71} - 60 q^{72} + 88 q^{73} + 120 q^{74} + 28 q^{75} + 100 q^{76} + 80 q^{77} - 16 q^{78} + 80 q^{79} + 56 q^{80} - 204 q^{81} + 72 q^{82} - 28 q^{83} + 60 q^{84} - 32 q^{85} - 76 q^{86} + 4 q^{87} - 268 q^{88} - 124 q^{89} + 32 q^{90} - 160 q^{91} + 40 q^{93} + 136 q^{94} - 112 q^{95} - 92 q^{96} + 128 q^{97} - 104 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1127, [\chi])\)\(^{\oplus 2}\)