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Properties

Label 3822.2.j
Level $3822$
Weight $2$
Character orbit 3822.j
Rep. character $\chi_{3822}(2713,\cdot)$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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

\( 188 q - 2 q^{3} + 188 q^{4} - 94 q^{9} + O(q^{10}) \) \( 188 q - 2 q^{3} + 188 q^{4} - 94 q^{9} - 8 q^{10} - 4 q^{11} - 2 q^{12} - 2 q^{13} + 188 q^{16} - 8 q^{17} - 6 q^{19} + 4 q^{22} + 32 q^{23} - 114 q^{25} + 4 q^{26} + 4 q^{27} - 12 q^{29} - 20 q^{31} - 94 q^{36} - 12 q^{37} + 4 q^{38} - 32 q^{39} - 8 q^{40} - 4 q^{41} - 26 q^{43} - 4 q^{44} - 32 q^{46} + 24 q^{47} - 2 q^{48} - 24 q^{50} + 16 q^{51} - 2 q^{52} - 36 q^{53} - 4 q^{55} + 36 q^{57} - 40 q^{58} + 32 q^{59} - 26 q^{61} - 20 q^{62} + 188 q^{64} - 16 q^{65} - 16 q^{66} + 92 q^{67} - 8 q^{68} - 8 q^{69} - 76 q^{71} + 6 q^{73} + 56 q^{74} + 44 q^{75} - 6 q^{76} + 24 q^{78} + 24 q^{79} - 94 q^{81} - 24 q^{82} + 112 q^{83} + 96 q^{85} + 4 q^{86} + 24 q^{87} + 4 q^{88} + 16 q^{89} + 16 q^{90} + 32 q^{92} - 56 q^{93} - 40 q^{94} + 64 q^{95} + 30 q^{97} + 8 q^{99} + O(q^{100}) \)

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

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