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Properties

Label 3850.2.fp
Level $3850$
Weight $2$
Character orbit 3850.fp
Rep. character $\chi_{3850}(233,\cdot)$
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.fp (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

\( 3840 q - 8 q^{5} + O(q^{10}) \) \( 3840 q - 8 q^{5} - 20 q^{10} - 16 q^{15} + 1920 q^{16} + 40 q^{17} - 24 q^{22} + 8 q^{23} - 24 q^{25} + 60 q^{28} + 16 q^{33} + 120 q^{35} + 960 q^{36} - 40 q^{42} - 32 q^{45} - 60 q^{47} + 120 q^{49} + 160 q^{50} - 40 q^{53} + 32 q^{55} + 240 q^{57} - 32 q^{58} + 120 q^{62} + 160 q^{63} - 32 q^{67} + 52 q^{70} - 32 q^{75} + 72 q^{77} - 80 q^{79} + 8 q^{80} - 480 q^{81} - 16 q^{82} + 120 q^{85} - 8 q^{88} + 16 q^{92} + 120 q^{93} - 56 q^{97} - 80 q^{98} + 120 q^{99} + O(q^{100}) \)

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

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