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Properties

Label 3822.2.en
Level $3822$
Weight $2$
Character orbit 3822.en
Rep. character $\chi_{3822}(71,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $6240$
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.en (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1911 \)
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 6240 12768
Cusp forms 18624 6240 12384
Eisenstein series 384 0 384

Trace form

\( 6240 q - 8 q^{7} + O(q^{10}) \) \( 6240 q - 8 q^{7} - 520 q^{16} + 16 q^{18} + 16 q^{19} + 16 q^{21} + 48 q^{27} + 8 q^{28} - 16 q^{31} + 72 q^{33} + 40 q^{37} + 84 q^{42} + 200 q^{45} - 24 q^{49} - 40 q^{52} - 24 q^{54} + 32 q^{55} + 32 q^{61} + 40 q^{63} + 32 q^{66} - 48 q^{67} + 168 q^{69} + 16 q^{72} - 128 q^{73} + 16 q^{76} + 64 q^{79} - 64 q^{81} + 96 q^{82} + 8 q^{84} + 112 q^{85} + 16 q^{87} + 32 q^{91} - 108 q^{93} - 160 q^{94} + 96 q^{97} + O(q^{100}) \)

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

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