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Properties

Label 3850.2.da
Level $3850$
Weight $2$
Character orbit 3850.da
Rep. character $\chi_{3850}(337,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1440$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3850.da (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3850, [\chi])\).

Total New Old
Modular forms 5824 1440 4384
Cusp forms 5696 1440 4256
Eisenstein series 128 0 128

Trace form

\( 1440 q + 8 q^{3} + O(q^{10}) \) \( 1440 q + 8 q^{3} - 8 q^{12} + 8 q^{15} + 360 q^{16} + 80 q^{19} + 8 q^{20} + 8 q^{22} - 8 q^{23} - 16 q^{27} + 40 q^{33} + 360 q^{36} - 8 q^{37} + 72 q^{38} + 24 q^{45} - 64 q^{47} - 8 q^{48} - 80 q^{53} - 120 q^{54} + 160 q^{59} + 40 q^{60} + 80 q^{62} - 40 q^{67} + 120 q^{69} + 16 q^{70} - 120 q^{71} - 120 q^{73} - 72 q^{75} + 16 q^{77} - 32 q^{78} - 1360 q^{81} + 48 q^{82} - 200 q^{83} + 40 q^{85} - 32 q^{88} + 8 q^{92} + 8 q^{93} + 72 q^{97} + 160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)