↑

Properties

Label 3822.2.eb
Level $3822$
Weight $2$
Character orbit 3822.eb
Rep. character $\chi_{3822}(145,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $3120$
Sturm bound $1568$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3822.eb (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

\( 3120 q - 260 q^{9} + O(q^{10}) \) \( 3120 q - 260 q^{9} - 16 q^{11} + 4 q^{12} - 8 q^{14} + 520 q^{16} - 28 q^{19} - 12 q^{21} + 8 q^{22} - 4 q^{28} + 8 q^{29} - 4 q^{31} + 48 q^{35} - 112 q^{37} + 8 q^{39} - 48 q^{41} - 60 q^{43} + 64 q^{44} + 16 q^{46} - 336 q^{47} + 4 q^{49} - 24 q^{52} - 8 q^{53} - 144 q^{55} + 144 q^{56} - 20 q^{57} - 112 q^{59} - 24 q^{61} - 72 q^{62} - 56 q^{65} + 4 q^{67} - 16 q^{70} - 24 q^{71} - 212 q^{73} - 40 q^{74} + 56 q^{75} + 32 q^{76} + 16 q^{79} + 260 q^{81} + 48 q^{82} - 48 q^{83} + 16 q^{84} - 104 q^{85} - 296 q^{86} + 96 q^{89} + 48 q^{91} + 56 q^{93} - 112 q^{94} - 380 q^{97} + 96 q^{98} - 8 q^{99} + O(q^{100}) \)

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

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