↑

Properties

Label 3381.2.bo
Level $3381$
Weight $2$
Character orbit 3381.bo
Rep. character $\chi_{3381}(229,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2688$
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.bo (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1127 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 5424 2688 2736
Cusp forms 5328 2688 2640
Eisenstein series 96 0 96

Trace form

\( 2688 q + 224 q^{4} - 224 q^{9} + O(q^{10}) \) \( 2688 q + 224 q^{4} - 224 q^{9} + 224 q^{16} + 8 q^{23} + 220 q^{25} - 28 q^{26} - 8 q^{29} + 12 q^{31} + 20 q^{32} - 88 q^{35} + 448 q^{36} + 56 q^{41} + 16 q^{46} + 12 q^{47} - 120 q^{49} - 464 q^{50} + 108 q^{52} + 56 q^{55} - 88 q^{58} - 148 q^{59} - 448 q^{64} - 100 q^{70} + 32 q^{71} + 36 q^{73} + 48 q^{75} + 84 q^{77} - 40 q^{78} + 224 q^{81} - 116 q^{82} - 64 q^{85} - 36 q^{87} - 68 q^{92} - 284 q^{94} + 20 q^{95} - 60 q^{96} + 280 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1127, [\chi])\)\(^{\oplus 2}\)