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Properties

Label 3822.2.dx
Level $3822$
Weight $2$
Character orbit 3822.dx
Rep. character $\chi_{3822}(43,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1584$
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.dx (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
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 1584 7920
Cusp forms 9312 1584 7728
Eisenstein series 192 0 192

Trace form

\( 1584 q - 132 q^{4} + 132 q^{9} + O(q^{10}) \) \( 1584 q - 132 q^{4} + 132 q^{9} - 8 q^{10} - 24 q^{11} + 16 q^{14} + 132 q^{16} + 8 q^{17} - 8 q^{22} + 280 q^{25} + 40 q^{26} - 8 q^{29} - 36 q^{35} - 132 q^{36} - 60 q^{37} + 40 q^{38} + 40 q^{39} - 16 q^{40} - 72 q^{41} + 8 q^{43} - 44 q^{49} + 80 q^{51} + 16 q^{53} - 76 q^{55} - 20 q^{56} - 40 q^{61} + 4 q^{62} + 264 q^{64} - 8 q^{65} - 32 q^{66} - 8 q^{68} - 72 q^{71} - 20 q^{74} - 16 q^{75} - 88 q^{77} - 40 q^{78} + 16 q^{79} + 132 q^{81} + 12 q^{84} - 120 q^{85} + 24 q^{87} - 20 q^{88} + 120 q^{89} + 16 q^{90} - 124 q^{91} + 48 q^{93} - 12 q^{94} + 112 q^{95} + 504 q^{97} - 24 q^{98} + O(q^{100}) \)

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

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