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Properties

Label 3822.2.l
Level $3822$
Weight $2$
Character orbit 3822.l
Rep. character $\chi_{3822}(295,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $188$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
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 188 1444
Cusp forms 1504 188 1316
Eisenstein series 128 0 128

Trace form

\( 188 q + 2 q^{2} - 94 q^{4} + 4 q^{5} - 4 q^{8} - 94 q^{9} + O(q^{10}) \) \( 188 q + 2 q^{2} - 94 q^{4} + 4 q^{5} - 4 q^{8} - 94 q^{9} - 6 q^{10} - 2 q^{13} - 4 q^{15} - 94 q^{16} - 10 q^{17} - 4 q^{18} + 16 q^{19} - 2 q^{20} - 16 q^{23} + 200 q^{25} + 18 q^{26} - 18 q^{29} + 4 q^{30} + 16 q^{31} + 2 q^{32} - 4 q^{33} - 4 q^{34} - 94 q^{36} - 50 q^{37} + 16 q^{38} + 24 q^{39} + 12 q^{40} + 6 q^{41} - 28 q^{43} - 2 q^{45} - 8 q^{46} - 32 q^{47} - 24 q^{50} + 4 q^{52} + 100 q^{53} - 8 q^{55} + 48 q^{57} - 46 q^{58} - 8 q^{59} + 8 q^{60} - 46 q^{61} + 8 q^{62} + 188 q^{64} - 66 q^{65} + 24 q^{66} + 56 q^{67} - 10 q^{68} - 20 q^{69} - 32 q^{71} + 2 q^{72} - 36 q^{73} - 34 q^{74} + 8 q^{75} + 16 q^{76} - 48 q^{79} - 2 q^{80} - 94 q^{81} + 2 q^{82} + 64 q^{83} + 62 q^{85} + 16 q^{86} + 12 q^{87} + 20 q^{89} + 12 q^{90} + 32 q^{92} + 56 q^{93} - 8 q^{94} + 56 q^{95} + 4 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3822, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1911, [\chi])\)\(^{\oplus 2}\)