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Properties

Label 3822.2.bb
Level $3822$
Weight $2$
Character orbit 3822.bb
Rep. character $\chi_{3822}(815,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $372$
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.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1568\)

Dimensions

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

Total New Old
Modular forms 1632 372 1260
Cusp forms 1504 372 1132
Eisenstein series 128 0 128

Trace form

\( 372 q - 372 q^{4} - 8 q^{9} + O(q^{10}) \) \( 372 q - 372 q^{4} - 8 q^{9} + 2 q^{13} - 24 q^{15} + 372 q^{16} - 4 q^{18} - 18 q^{19} - 182 q^{25} + 14 q^{30} - 12 q^{31} - 72 q^{33} + 8 q^{36} + 44 q^{37} + 62 q^{39} - 30 q^{43} - 16 q^{46} - 14 q^{51} - 2 q^{52} + 24 q^{55} - 16 q^{57} + 16 q^{58} + 24 q^{60} - 78 q^{61} - 372 q^{64} + 24 q^{66} - 12 q^{67} - 30 q^{69} + 4 q^{72} + 54 q^{73} + 18 q^{76} + 8 q^{78} + 28 q^{79} - 4 q^{81} + 24 q^{82} + 16 q^{85} + 16 q^{93} + 24 q^{94} - 66 q^{97} + O(q^{100}) \)

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

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