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Properties

Label 3800.2.ec
Level $3800$
Weight $2$
Character orbit 3800.ec
Rep. character $\chi_{3800}(193,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1080$
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.ec (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 7488 1080 6408
Cusp forms 6912 1080 5832
Eisenstein series 576 0 576

Trace form

\( 1080 q + O(q^{10}) \) \( 1080 q - 24 q^{23} - 72 q^{33} + 72 q^{41} - 48 q^{43} - 24 q^{47} - 36 q^{51} + 24 q^{57} - 108 q^{63} + 144 q^{67} + 72 q^{77} + 96 q^{81} + 36 q^{83} + 72 q^{87} - 144 q^{91} - 36 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1900, [\chi])\)\(^{\oplus 2}\)