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Properties

Label 3822.2.dd
Level $3822$
Weight $2$
Character orbit 3822.dd
Rep. character $\chi_{3822}(205,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1560$
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.dd (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 1560 7944
Cusp forms 9312 1560 7752
Eisenstein series 192 0 192

Trace form

\( 1560 q + 2 q^{3} + 260 q^{4} + 2 q^{7} + 130 q^{9} + O(q^{10}) \) \( 1560 q + 2 q^{3} + 260 q^{4} + 2 q^{7} + 130 q^{9} - 8 q^{10} - 12 q^{11} - 2 q^{12} + 2 q^{13} - 8 q^{14} - 260 q^{16} + 8 q^{17} - 6 q^{19} - 14 q^{21} + 4 q^{22} - 126 q^{25} - 32 q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{29} - 36 q^{35} - 130 q^{36} + 14 q^{37} + 52 q^{38} - 4 q^{39} + 8 q^{40} + 36 q^{41} + 10 q^{43} + 12 q^{44} - 180 q^{47} - 12 q^{48} - 58 q^{49} + 104 q^{51} + 12 q^{52} + 4 q^{53} - 88 q^{55} - 20 q^{56} - 68 q^{61} - 32 q^{62} + 24 q^{63} + 260 q^{64} - 32 q^{65} + 16 q^{66} - 8 q^{68} - 24 q^{69} - 48 q^{70} + 36 q^{71} + 210 q^{73} - 20 q^{74} + 12 q^{75} + 6 q^{76} + 152 q^{77} + 104 q^{78} + 32 q^{79} + 130 q^{81} - 24 q^{82} + 14 q^{84} - 24 q^{85} - 216 q^{86} + 24 q^{87} + 52 q^{88} + 16 q^{90} + 12 q^{91} + 96 q^{94} + 112 q^{95} - 150 q^{97} + 72 q^{98} + O(q^{100}) \)

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

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