Properties

Label 3850.2.di
Level $3850$
Weight $2$
Character orbit 3850.di
Rep. character $\chi_{3850}(57,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $864$
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.di (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 5952 864 5088
Cusp forms 5568 864 4704
Eisenstein series 384 0 384

Trace form

\( 864 q - 8 q^{3} + O(q^{10}) \) \( 864 q - 8 q^{3} + 16 q^{11} - 32 q^{12} + 216 q^{16} - 8 q^{22} - 32 q^{23} + 16 q^{27} + 64 q^{31} - 40 q^{33} + 184 q^{36} + 8 q^{37} - 72 q^{38} + 160 q^{46} + 24 q^{47} + 8 q^{48} - 80 q^{51} + 80 q^{52} + 80 q^{53} + 160 q^{57} + 80 q^{62} + 216 q^{66} + 160 q^{67} + 48 q^{71} - 16 q^{77} + 32 q^{78} + 280 q^{81} + 32 q^{82} + 136 q^{86} - 8 q^{88} - 144 q^{91} - 8 q^{92} + 112 q^{93} + 88 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(770, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)