Properties

Label 3380.2.cn
Level $3380$
Weight $2$
Character orbit 3380.cn
Rep. character $\chi_{3380}(101,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $1440$
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.cn (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(1092\)

Dimensions

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

Total New Old
Modular forms 13248 1440 11808
Cusp forms 12960 1440 11520
Eisenstein series 288 0 288

Trace form

\( 1440 q + 2 q^{3} - 6 q^{7} + 60 q^{9} + O(q^{10}) \) \( 1440 q + 2 q^{3} - 6 q^{7} + 60 q^{9} - 12 q^{11} - 70 q^{13} + 6 q^{15} - 10 q^{17} + 6 q^{23} + 120 q^{25} - 4 q^{27} + 4 q^{29} - 52 q^{31} + 6 q^{33} + 6 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{41} - 10 q^{43} - 156 q^{47} - 78 q^{49} - 8 q^{51} - 32 q^{53} - 4 q^{55} + 78 q^{57} + 24 q^{59} + 4 q^{61} - 24 q^{63} - 50 q^{67} + 20 q^{69} - 120 q^{71} - 2 q^{75} + 4 q^{77} + 8 q^{79} + 56 q^{81} - 18 q^{85} + 14 q^{87} + 24 q^{89} - 104 q^{91} + 54 q^{93} + 30 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1690, [\chi])\)\(^{\oplus 2}\)