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Properties

Label 3381.2.s
Level $3381$
Weight $2$
Character orbit 3381.s
Rep. character $\chi_{3381}(160,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1344$
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.s (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1127 \)
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 1344 1368
Cusp forms 2664 1344 1320
Eisenstein series 48 0 48

Trace form

\( 1344 q - 224 q^{4} + 224 q^{9} + O(q^{10}) \) \( 1344 q - 224 q^{4} + 224 q^{9} - 224 q^{16} + 16 q^{23} - 232 q^{25} - 56 q^{26} + 8 q^{29} + 40 q^{32} + 40 q^{35} + 224 q^{36} + 28 q^{41} + 32 q^{46} - 72 q^{49} + 464 q^{50} + 28 q^{55} - 8 q^{58} + 28 q^{59} - 224 q^{64} + 124 q^{70} - 32 q^{71} - 84 q^{73} - 12 q^{77} + 40 q^{78} - 224 q^{81} - 280 q^{82} + 64 q^{85} + 26 q^{92} - 364 q^{94} + 40 q^{95} + 224 q^{98} + O(q^{100}) \)

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

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