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Properties

Label 3800.2.q
Level $3800$
Weight $2$
Character orbit 3800.q
Rep. character $\chi_{3800}(201,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $190$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 1248 190 1058
Cusp forms 1152 190 962
Eisenstein series 96 0 96

Trace form

\( 190 q - 3 q^{3} - 4 q^{7} - 92 q^{9} + O(q^{10}) \) \( 190 q - 3 q^{3} - 4 q^{7} - 92 q^{9} - 2 q^{11} + 4 q^{13} - 8 q^{17} + 5 q^{19} - 2 q^{21} + 14 q^{23} + 18 q^{27} - 8 q^{29} - 24 q^{31} + 7 q^{33} - 32 q^{37} - 24 q^{39} - 13 q^{41} + 18 q^{43} + 8 q^{47} + 198 q^{49} - 2 q^{51} + 16 q^{53} + 34 q^{57} + 5 q^{59} + 12 q^{61} - 12 q^{63} - 19 q^{67} + 20 q^{69} - 3 q^{73} - 36 q^{77} + 26 q^{79} - 51 q^{81} + 6 q^{83} - 72 q^{87} - 24 q^{89} - 20 q^{91} + 48 q^{93} + 11 q^{97} + 12 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)