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Properties

Label 3822.2.cv
Level $3822$
Weight $2$
Character orbit 3822.cv
Rep. character $\chi_{3822}(265,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1536$
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.cv (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(1568\)

Dimensions

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

Total New Old
Modular forms 9504 1536 7968
Cusp forms 9312 1536 7776
Eisenstein series 192 0 192

Trace form

\( 1536 q + 4 q^{7} + 256 q^{9} + O(q^{10}) \) \( 1536 q + 4 q^{7} + 256 q^{9} + 16 q^{11} + 8 q^{14} + 256 q^{16} + 12 q^{21} + 16 q^{22} + 4 q^{28} + 16 q^{29} + 96 q^{35} + 108 q^{37} + 100 q^{39} - 40 q^{44} - 16 q^{46} - 168 q^{47} + 28 q^{52} - 16 q^{53} - 336 q^{55} + 24 q^{57} - 56 q^{59} + 24 q^{63} + 32 q^{65} - 56 q^{67} - 56 q^{70} - 48 q^{71} + 168 q^{73} - 80 q^{74} + 32 q^{79} - 256 q^{81} + 12 q^{84} + 32 q^{85} - 88 q^{86} + 36 q^{91} + 56 q^{93} + 112 q^{94} + 48 q^{98} - 16 q^{99} + O(q^{100}) \)

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

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