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Properties

Label 3380.2.bf
Level $3380$
Weight $2$
Character orbit 3380.bf
Rep. character $\chi_{3380}(657,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $308$
Sturm bound $1092$

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Defining parameters

Level: \( N \) \(=\) \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3380.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1092\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3380, [\chi])\).

Total New Old
Modular forms 2352 308 2044
Cusp forms 2016 308 1708
Eisenstein series 336 0 336

Trace form

\( 308 q + 2 q^{5} - 12 q^{9} + O(q^{10}) \) \( 308 q + 2 q^{5} - 12 q^{9} - 12 q^{15} + 4 q^{17} + 12 q^{19} - 12 q^{21} - 16 q^{23} - 6 q^{25} + 48 q^{27} - 24 q^{31} + 48 q^{33} + 24 q^{35} - 16 q^{37} - 22 q^{41} + 4 q^{43} - 12 q^{45} + 32 q^{47} - 134 q^{49} + 2 q^{53} + 32 q^{55} - 8 q^{59} + 20 q^{61} + 96 q^{63} + 48 q^{67} - 40 q^{69} + 16 q^{75} + 40 q^{77} + 190 q^{81} + 64 q^{83} - 58 q^{85} - 68 q^{87} - 30 q^{89} - 16 q^{93} - 8 q^{95} + 56 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3380, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1690, [\chi])\)\(^{\oplus 2}\)