↑

Properties

Label 3822.2.ek
Level $3822$
Weight $2$
Character orbit 3822.ek
Rep. character $\chi_{3822}(223,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $3168$
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.ek (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 3168 15840
Cusp forms 18624 3168 15456
Eisenstein series 384 0 384

Trace form

\( 3168 q - 264 q^{9} + O(q^{10}) \) \( 3168 q - 264 q^{9} - 16 q^{11} + 16 q^{14} - 264 q^{16} - 8 q^{21} - 16 q^{22} - 16 q^{29} + 48 q^{35} + 32 q^{37} - 80 q^{39} - 48 q^{43} + 40 q^{44} + 16 q^{46} + 168 q^{47} + 24 q^{49} - 32 q^{53} - 168 q^{55} + 144 q^{56} - 16 q^{57} + 56 q^{59} - 32 q^{65} + 48 q^{67} - 16 q^{70} + 48 q^{71} - 168 q^{73} - 40 q^{74} + 64 q^{79} + 264 q^{81} + 16 q^{84} + 208 q^{85} + 184 q^{86} + 16 q^{91} + 48 q^{93} + 56 q^{94} + 192 q^{95} + 16 q^{99} + O(q^{100}) \)

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

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