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Properties

Label 3380.2.cf
Level $3380$
Weight $2$
Character orbit 3380.cf
Rep. character $\chi_{3380}(57,\cdot)$
Character field $\Q(\zeta_{52})$
Dimension $2184$
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.cf (of order \(52\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 845 \)
Character field: \(\Q(\zeta_{52})\)
Sturm bound: \(1092\)

Dimensions

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

Total New Old
Modular forms 13248 2184 11064
Cusp forms 12960 2184 10776
Eisenstein series 288 0 288

Trace form

\( 2184 q + O(q^{10}) \) \( 2184 q + 92 q^{15} - 2 q^{17} - 12 q^{19} + 12 q^{21} + 16 q^{23} + 10 q^{25} - 52 q^{33} + 12 q^{39} - 2 q^{41} + 8 q^{43} - 112 q^{45} + 130 q^{47} + 226 q^{49} - 116 q^{53} - 24 q^{55} + 4 q^{57} + 16 q^{59} + 8 q^{61} + 154 q^{63} - 30 q^{65} - 176 q^{67} - 16 q^{69} + 12 q^{71} + 32 q^{73} - 154 q^{75} - 24 q^{77} + 190 q^{81} + 260 q^{83} + 14 q^{85} + 80 q^{87} - 18 q^{89} - 16 q^{91} + 32 q^{95} + 140 q^{97} + 20 q^{99} + O(q^{100}) \)

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

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