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Properties

Label 3850.2.fn
Level $3850$
Weight $2$
Character orbit 3850.fn
Rep. character $\chi_{3850}(831,\cdot)$
Character field $\Q(\zeta_{30})$
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.fn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1925 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 1920 q - 240 q^{4} - 18 q^{5} + 960 q^{9} + O(q^{10}) \) \( 1920 q - 240 q^{4} - 18 q^{5} + 960 q^{9} - 30 q^{10} + 6 q^{11} - 8 q^{15} + 240 q^{16} + 24 q^{22} - 8 q^{23} - 2 q^{25} - 10 q^{28} - 6 q^{31} - 108 q^{33} + 20 q^{35} - 480 q^{36} - 10 q^{37} + 6 q^{42} + 4 q^{44} - 42 q^{45} - 24 q^{47} - 12 q^{49} - 60 q^{53} - 120 q^{57} + 32 q^{58} - 4 q^{60} - 130 q^{63} + 480 q^{64} - 48 q^{66} + 64 q^{67} - 60 q^{70} - 64 q^{71} + 180 q^{75} - 48 q^{77} + 40 q^{79} - 12 q^{80} - 1024 q^{81} + 48 q^{82} + 100 q^{85} + 6 q^{86} - 8 q^{88} - 120 q^{89} - 24 q^{91} + 24 q^{92} + 8 q^{93} - 80 q^{95} + 40 q^{98} - 36 q^{99} + O(q^{100}) \)

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

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