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Properties

Label 3800.2.ei
Level $3800$
Weight $2$
Character orbit 3800.ei
Rep. character $\chi_{3800}(81,\cdot)$
Character field $\Q(\zeta_{45})$
Dimension $3600$
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.ei (of order \(45\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{45})\)
Sturm bound: \(1200\)

Dimensions

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

Total New Old
Modular forms 14592 3600 10992
Cusp forms 14208 3600 10608
Eisenstein series 384 0 384

Trace form

\( 3600 q + O(q^{10}) \) \( 3600 q + 48 q^{15} - 24 q^{23} - 12 q^{25} + 72 q^{33} + 24 q^{35} - 192 q^{43} - 72 q^{45} + 36 q^{47} - 1800 q^{49} + 36 q^{55} + 168 q^{57} + 36 q^{59} + 108 q^{63} - 144 q^{67} - 48 q^{69} + 36 q^{71} - 72 q^{77} - 54 q^{83} + 12 q^{85} + 108 q^{87} - 108 q^{93} + 78 q^{95} + O(q^{100}) \)

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

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