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Properties

Label 3822.2.cq
Level $3822$
Weight $2$
Character orbit 3822.cq
Rep. character $\chi_{3822}(211,\cdot)$
Character field $\Q(\zeta_{21})$
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.cq (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{21})\)
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

\( 1584 q + 132 q^{4} + 132 q^{9} + O(q^{10}) \) \( 1584 q + 132 q^{4} + 132 q^{9} - 8 q^{10} + 8 q^{11} + 132 q^{16} - 8 q^{17} + 16 q^{19} - 8 q^{21} - 8 q^{22} - 280 q^{25} - 40 q^{26} - 8 q^{29} + 32 q^{31} - 12 q^{35} + 132 q^{36} - 68 q^{37} - 40 q^{38} + 40 q^{39} + 16 q^{40} + 8 q^{41} + 8 q^{43} + 40 q^{44} - 16 q^{46} + 120 q^{47} + 52 q^{49} - 80 q^{51} + 16 q^{53} - 76 q^{55} - 28 q^{56} - 16 q^{57} + 40 q^{59} - 8 q^{61} + 44 q^{62} - 264 q^{64} - 56 q^{65} + 32 q^{66} - 48 q^{67} - 8 q^{68} - 32 q^{69} + 16 q^{70} + 24 q^{71} + 184 q^{73} - 20 q^{74} + 16 q^{75} + 16 q^{76} + 184 q^{77} + 40 q^{78} + 48 q^{79} + 132 q^{81} + 64 q^{83} + 4 q^{84} - 88 q^{85} + 184 q^{86} + 24 q^{87} + 20 q^{88} + 40 q^{89} + 16 q^{90} + 76 q^{91} - 44 q^{94} - 48 q^{95} - 152 q^{97} + 24 q^{98} - 16 q^{99} + O(q^{100}) \)

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

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