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Properties

Label 3762.2.ek
Level $3762$
Weight $2$
Character orbit 3762.ek
Rep. character $\chi_{3762}(17,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $1920$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3762.ek (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 627 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3762, [\chi])\).

Total New Old
Modular forms 17664 1920 15744
Cusp forms 16896 1920 14976
Eisenstein series 768 0 768

Trace form

\( 1920 q + O(q^{10}) \) \( 1920 q + 24 q^{22} - 216 q^{25} + 96 q^{34} - 48 q^{37} - 312 q^{49} + 408 q^{55} + 96 q^{58} + 240 q^{64} - 96 q^{67} - 96 q^{70} - 120 q^{85} - 144 q^{91} + 240 q^{94} - 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3762, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3762, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3762, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(627, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1254, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1881, [\chi])\)\(^{\oplus 2}\)