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Properties

Label 3850.2.gl
Level $3850$
Weight $2$
Character orbit 3850.gl
Rep. character $\chi_{3850}(213,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3840$
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.gl (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1925 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 11648 3840 7808
Cusp forms 11392 3840 7552
Eisenstein series 256 0 256

Trace form

\( 3840 q - 36 q^{5} + 24 q^{7} + O(q^{10}) \) \( 3840 q - 36 q^{5} + 24 q^{7} - 36 q^{10} + 16 q^{15} - 480 q^{16} + 8 q^{22} + 8 q^{23} + 36 q^{25} - 28 q^{28} - 16 q^{30} - 48 q^{33} - 40 q^{35} + 960 q^{36} + 52 q^{37} - 24 q^{42} + 80 q^{43} + 96 q^{45} - 24 q^{47} - 120 q^{49} + 64 q^{50} - 60 q^{53} + 64 q^{57} + 32 q^{58} - 64 q^{63} + 32 q^{65} + 32 q^{67} + 40 q^{70} + 120 q^{73} - 336 q^{75} - 16 q^{77} - 80 q^{79} + 24 q^{80} + 1920 q^{81} + 48 q^{82} + 128 q^{85} - 24 q^{87} - 36 q^{88} + 24 q^{92} - 88 q^{93} - 24 q^{95} - 48 q^{98} + 120 q^{99} + O(q^{100}) \)

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

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