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Properties

Label 3800.2.cn
Level $3800$
Weight $2$
Character orbit 3800.cn
Rep. character $\chi_{3800}(121,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1200$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3800.cn (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3800, [\chi])\).

Total New Old
Modular forms 4864 1200 3664
Cusp forms 4736 1200 3536
Eisenstein series 128 0 128

Trace form

\( 1200 q + 150 q^{9} + O(q^{10}) \) \( 1200 q + 150 q^{9} - 16 q^{15} - 8 q^{21} - 10 q^{23} + 4 q^{25} - 12 q^{29} + 12 q^{33} + 10 q^{35} - 16 q^{37} + 24 q^{39} - 16 q^{41} - 32 q^{43} - 32 q^{45} - 12 q^{47} + 1200 q^{49} - 96 q^{51} + 26 q^{55} - 88 q^{57} + 24 q^{59} - 12 q^{63} + 12 q^{65} - 24 q^{67} + 32 q^{69} - 12 q^{71} + 48 q^{73} + 36 q^{75} - 56 q^{77} + 78 q^{81} + 20 q^{83} - 6 q^{85} + 204 q^{87} - 24 q^{89} + 24 q^{91} - 156 q^{93} - 98 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3800, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1900, [\chi])\)\(^{\oplus 2}\)