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Properties

Label 3822.2.i
Level $3822$
Weight $2$
Character orbit 3822.i
Rep. character $\chi_{3822}(79,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $160$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1568\)

Dimensions

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

Total New Old
Modular forms 1632 160 1472
Cusp forms 1504 160 1344
Eisenstein series 128 0 128

Trace form

\( 160 q - 80 q^{4} - 8 q^{5} - 8 q^{6} - 80 q^{9} + O(q^{10}) \) \( 160 q - 80 q^{4} - 8 q^{5} - 8 q^{6} - 80 q^{9} - 4 q^{10} - 8 q^{11} - 8 q^{13} + 8 q^{15} - 80 q^{16} + 12 q^{17} + 8 q^{19} + 16 q^{20} - 16 q^{22} + 8 q^{23} + 4 q^{24} - 60 q^{25} + 8 q^{29} + 16 q^{30} - 20 q^{31} + 4 q^{33} - 16 q^{34} + 160 q^{36} + 8 q^{37} - 20 q^{38} - 4 q^{40} - 64 q^{41} + 16 q^{43} - 8 q^{44} - 8 q^{45} + 16 q^{46} - 24 q^{47} + 32 q^{50} - 8 q^{51} + 4 q^{52} - 4 q^{53} + 4 q^{54} - 8 q^{55} - 32 q^{57} - 12 q^{58} - 4 q^{60} + 4 q^{61} - 16 q^{62} + 160 q^{64} + 16 q^{65} - 16 q^{67} + 12 q^{68} + 32 q^{69} - 32 q^{71} + 16 q^{73} + 16 q^{74} - 16 q^{76} + 12 q^{79} - 8 q^{80} - 80 q^{81} + 32 q^{86} - 4 q^{87} + 8 q^{88} + 16 q^{89} + 8 q^{90} - 16 q^{92} + 16 q^{93} - 4 q^{94} + 56 q^{95} + 4 q^{96} + 40 q^{97} + 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3822, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1911, [\chi])\)\(^{\oplus 2}\)