Properties

Label 3822.2.ch
Level $3822$
Weight $2$
Character orbit 3822.ch
Rep. character $\chi_{3822}(1501,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $376$
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.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 376 2888
Cusp forms 3008 376 2632
Eisenstein series 256 0 256

Trace form

\( 376 q + 188 q^{9} + O(q^{10}) \) \( 376 q + 188 q^{9} - 16 q^{11} + 4 q^{12} - 376 q^{16} - 28 q^{19} + 8 q^{22} + 40 q^{29} - 4 q^{31} - 84 q^{37} + 64 q^{39} - 48 q^{41} + 108 q^{43} + 8 q^{44} - 48 q^{50} - 48 q^{51} + 4 q^{52} + 24 q^{53} + 24 q^{55} + 36 q^{57} + 64 q^{58} - 24 q^{61} - 72 q^{62} - 120 q^{65} - 4 q^{67} + 40 q^{71} - 44 q^{73} - 80 q^{74} + 56 q^{75} + 32 q^{76} + 32 q^{78} - 16 q^{79} - 188 q^{81} + 48 q^{82} - 48 q^{83} + 120 q^{85} + 40 q^{86} + 96 q^{89} + 64 q^{92} - 56 q^{93} + 124 q^{97} - 8 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3822, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1911, [\chi])\)\(^{\oplus 2}\)