Properties

Label 3381.2.i
Level $3381$
Weight $2$
Character orbit 3381.i
Rep. character $\chi_{3381}(1243,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $292$
Sturm bound $896$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 928 292 636
Cusp forms 864 292 572
Eisenstein series 64 0 64

Trace form

\( 292 q - 2 q^{3} - 144 q^{4} + 8 q^{6} - 24 q^{8} - 146 q^{9} + O(q^{10}) \) \( 292 q - 2 q^{3} - 144 q^{4} + 8 q^{6} - 24 q^{8} - 146 q^{9} + 16 q^{10} - 4 q^{12} + 4 q^{13} - 8 q^{15} - 124 q^{16} + 8 q^{17} + 6 q^{19} + 16 q^{20} - 48 q^{22} - 130 q^{25} - 32 q^{26} + 4 q^{27} - 24 q^{29} - 22 q^{31} + 24 q^{32} + 12 q^{33} + 16 q^{34} + 288 q^{36} + 38 q^{37} + 20 q^{38} + 26 q^{39} + 36 q^{40} - 8 q^{41} - 44 q^{43} + 16 q^{44} + 8 q^{47} + 16 q^{48} - 120 q^{50} + 80 q^{53} - 4 q^{54} + 48 q^{55} - 68 q^{57} + 32 q^{58} + 20 q^{59} - 36 q^{60} + 16 q^{61} - 24 q^{62} + 200 q^{64} + 28 q^{65} + 24 q^{66} + 22 q^{67} + 12 q^{68} + 16 q^{69} + 56 q^{71} + 12 q^{72} - 18 q^{73} + 76 q^{74} - 14 q^{75} - 24 q^{76} + 56 q^{78} + 22 q^{79} - 92 q^{80} - 146 q^{81} - 24 q^{82} - 56 q^{83} - 56 q^{85} + 28 q^{86} - 20 q^{87} + 56 q^{88} - 32 q^{90} + 34 q^{93} + 20 q^{94} - 8 q^{95} - 4 q^{96} - 40 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1127, [\chi])\)\(^{\oplus 2}\)