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Properties

Label 3850.2.ca
Level $3850$
Weight $2$
Character orbit 3850.ca
Rep. character $\chi_{3850}(41,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $960$
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.ca (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1925 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2912 960 1952
Cusp forms 2848 960 1888
Eisenstein series 64 0 64

Trace form

\( 960 q - 960 q^{4} + 240 q^{9} + O(q^{10}) \) \( 960 q - 960 q^{4} + 240 q^{9} - 8 q^{11} + 8 q^{15} + 960 q^{16} + 20 q^{22} - 16 q^{23} - 28 q^{25} + 30 q^{35} - 240 q^{36} - 8 q^{37} - 6 q^{42} + 8 q^{44} - 20 q^{46} + 12 q^{49} - 80 q^{50} + 80 q^{53} + 180 q^{57} + 64 q^{58} - 8 q^{60} + 90 q^{63} - 960 q^{64} - 16 q^{67} - 14 q^{70} + 8 q^{71} + 58 q^{77} - 80 q^{79} - 208 q^{81} - 120 q^{85} - 48 q^{86} - 20 q^{88} + 22 q^{91} + 16 q^{92} - 8 q^{93} + 80 q^{95} + 40 q^{98} - 108 q^{99} + O(q^{100}) \)

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

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