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Properties

Label 3800.2.by
Level $3800$
Weight $2$
Character orbit 3800.by
Rep. character $\chi_{3800}(609,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $536$
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.by (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 2432 536 1896
Cusp forms 2368 536 1832
Eisenstein series 64 0 64

Trace form

\( 536 q - 4 q^{5} + 130 q^{9} + O(q^{10}) \) \( 536 q - 4 q^{5} + 130 q^{9} - 12 q^{11} + 8 q^{15} + 6 q^{19} + 30 q^{23} - 4 q^{25} + 16 q^{29} - 12 q^{31} - 18 q^{35} + 80 q^{37} - 16 q^{41} + 8 q^{45} - 480 q^{49} + 24 q^{51} + 60 q^{53} + 6 q^{55} - 28 q^{61} + 16 q^{65} + 24 q^{69} + 4 q^{75} - 32 q^{79} - 118 q^{81} - 30 q^{83} - 110 q^{85} - 24 q^{89} + 32 q^{91} - 60 q^{97} - 184 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1900, [\chi])\)\(^{\oplus 2}\)