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Properties

Label 3850.2.db
Level $3850$
Weight $2$
Character orbit 3850.db
Rep. character $\chi_{3850}(97,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1920$
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.db (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1925 \)
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 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

Trace form

\( 1920 q - 24 q^{7} + O(q^{10}) \) \( 1920 q - 24 q^{7} - 16 q^{15} + 480 q^{16} + 16 q^{22} + 16 q^{23} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 480 q^{36} + 56 q^{37} + 24 q^{42} - 80 q^{43} + 120 q^{49} - 64 q^{50} - 120 q^{53} - 112 q^{57} + 64 q^{58} - 32 q^{63} - 32 q^{65} - 80 q^{67} + 32 q^{70} + 16 q^{77} - 160 q^{79} - 1920 q^{81} + 40 q^{85} + 24 q^{88} - 24 q^{92} + 88 q^{93} + 336 q^{95} + 48 q^{98} + 360 q^{99} + O(q^{100}) \)

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

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