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Properties

Label 3822.2.bn
Level $3822$
Weight $2$
Character orbit 3822.bn
Rep. character $\chi_{3822}(2285,\cdot)$
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.bn (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

\( 372 q - 186 q^{4} - 16 q^{9} + O(q^{10}) \) \( 372 q - 186 q^{4} - 16 q^{9} + 2 q^{13} + 24 q^{15} - 186 q^{16} + 36 q^{18} + 28 q^{19} + 182 q^{25} - 4 q^{30} - 16 q^{31} - 24 q^{33} + 8 q^{36} + 42 q^{37} - 20 q^{39} - 14 q^{43} + 24 q^{46} - 18 q^{51} + 14 q^{52} + 18 q^{54} - 24 q^{55} - 24 q^{60} + 372 q^{64} - 24 q^{66} + 54 q^{69} + 2 q^{73} + 108 q^{75} - 14 q^{76} + 8 q^{78} + 84 q^{79} + 24 q^{81} + 120 q^{85} + 24 q^{87} + 36 q^{93} - 14 q^{97} + O(q^{100}) \)

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

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