Properties

Label 3822.2.ej
Level $3822$
Weight $2$
Character orbit 3822.ej
Rep. character $\chi_{3822}(115,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $3120$
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.ej (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(1568\)

Dimensions

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

Total New Old
Modular forms 19008 3120 15888
Cusp forms 18624 3120 15504
Eisenstein series 384 0 384

Trace form

\( 3120 q - 4 q^{7} + 520 q^{9} + O(q^{10}) \) \( 3120 q - 4 q^{7} + 520 q^{9} + 8 q^{11} - 4 q^{12} - 8 q^{14} - 260 q^{16} + 4 q^{19} + 16 q^{21} + 8 q^{22} + 8 q^{29} + 4 q^{31} - 96 q^{35} - 12 q^{37} - 104 q^{39} + 48 q^{41} - 60 q^{43} + 40 q^{44} - 8 q^{46} + 168 q^{47} - 28 q^{49} - 4 q^{52} - 8 q^{53} + 312 q^{55} + 144 q^{56} - 20 q^{57} + 56 q^{59} + 72 q^{62} - 24 q^{63} + 40 q^{65} - 8 q^{67} - 24 q^{68} - 112 q^{70} - 24 q^{71} + 224 q^{73} + 104 q^{74} + 28 q^{75} - 32 q^{76} + 16 q^{79} - 520 q^{81} + 96 q^{82} + 48 q^{83} + 24 q^{84} - 104 q^{85} + 136 q^{86} + 72 q^{87} + 96 q^{89} + 40 q^{91} - 4 q^{93} + 56 q^{94} + 96 q^{95} + 380 q^{97} - 8 q^{99} + O(q^{100}) \)

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

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