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Properties

Label 3822.2.ci
Level $3822$
Weight $2$
Character orbit 3822.ci
Rep. character $\chi_{3822}(275,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $744$
Sturm bound $1568$

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Defining parameters

Level: \( N \) \(=\) \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3822.ci (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1568\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3822, [\chi])\).

Total New Old
Modular forms 3264 744 2520
Cusp forms 3008 744 2264
Eisenstein series 256 0 256

Trace form

\( 744 q + O(q^{10}) \) \( 744 q - 744 q^{16} + 24 q^{18} - 36 q^{19} - 24 q^{27} + 48 q^{30} + 36 q^{31} - 12 q^{33} - 48 q^{36} - 44 q^{37} + 16 q^{39} + 84 q^{43} + 40 q^{45} - 16 q^{46} + 20 q^{52} + 12 q^{54} - 16 q^{55} + 16 q^{57} - 16 q^{58} - 48 q^{60} + 32 q^{61} - 16 q^{66} - 28 q^{67} - 84 q^{69} - 84 q^{73} + 48 q^{76} + 16 q^{78} - 80 q^{79} + 16 q^{81} + 48 q^{82} + 248 q^{85} + 96 q^{87} + 32 q^{93} - 32 q^{94} + 100 q^{97} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3822, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3822, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3822, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1911, [\chi])\)\(^{\oplus 2}\)