↑

Properties

Label 3822.2.dc
Level $3822$
Weight $2$
Character orbit 3822.dc
Rep. character $\chi_{3822}(101,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $3144$
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.dc (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1911 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1568\)

Dimensions

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

Total New Old
Modular forms 9504 3144 6360
Cusp forms 9312 3144 6168
Eisenstein series 192 0 192

Trace form

\( 3144 q + 262 q^{4} - 2 q^{7} + O(q^{10}) \) \( 3144 q + 262 q^{4} - 2 q^{7} + 2 q^{13} + 262 q^{16} + 12 q^{18} + 28 q^{19} - 266 q^{25} + 4 q^{28} + 12 q^{30} - 16 q^{31} - 24 q^{33} + 154 q^{37} - 4 q^{39} + 26 q^{42} + 6 q^{43} - 210 q^{45} - 42 q^{49} + 6 q^{51} - 42 q^{52} + 18 q^{54} - 24 q^{55} + 42 q^{61} - 12 q^{63} - 524 q^{64} - 24 q^{66} + 26 q^{69} + 2 q^{73} + 66 q^{75} - 14 q^{76} - 16 q^{78} - 20 q^{79} - 12 q^{81} + 144 q^{85} - 32 q^{87} - 42 q^{90} + 144 q^{91} - 12 q^{93} + 112 q^{94} - 14 q^{97} + O(q^{100}) \)

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

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