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Properties

Label 3762.2.cd
Level $3762$
Weight $2$
Character orbit 3762.cd
Rep. character $\chi_{3762}(263,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1440$
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.cd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1881 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 4368 1440 2928
Cusp forms 4272 1440 2832
Eisenstein series 96 0 96

Trace form

\( 1440 q + 6 q^{3} - 6 q^{9} + O(q^{10}) \) \( 1440 q + 6 q^{3} - 6 q^{9} - 9 q^{22} - 6 q^{27} + 3 q^{33} - 6 q^{36} - 18 q^{38} + 36 q^{45} + 6 q^{48} - 1440 q^{49} + 306 q^{59} - 720 q^{64} + 114 q^{66} + 18 q^{67} + 36 q^{69} + 138 q^{81} + 18 q^{82} - 168 q^{93} - 18 q^{97} + 51 q^{99} + O(q^{100}) \)

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

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