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Properties

Label 3822.2.cr
Level $3822$
Weight $2$
Character orbit 3822.cr
Rep. character $\chi_{3822}(445,\cdot)$
Character field $\Q(\zeta_{21})$
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.cr (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 1560 7944
Cusp forms 9312 1560 7752
Eisenstein series 192 0 192

Trace form

\( 1560 q + 4 q^{3} + 130 q^{4} - 2 q^{7} - 260 q^{9} + O(q^{10}) \) \( 1560 q + 4 q^{3} + 130 q^{4} - 2 q^{7} - 260 q^{9} + 16 q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{13} + 130 q^{16} + 4 q^{17} + 12 q^{19} + 2 q^{21} + 4 q^{22} + 126 q^{25} + 32 q^{26} + 4 q^{27} + 4 q^{28} + 4 q^{29} - 20 q^{31} + 60 q^{35} + 130 q^{36} - 22 q^{37} - 52 q^{38} + 52 q^{39} - 8 q^{40} - 4 q^{41} + 10 q^{43} + 52 q^{44} + 8 q^{46} - 60 q^{47} + 12 q^{48} + 62 q^{49} - 104 q^{51} - 2 q^{52} + 4 q^{53} + 164 q^{55} - 16 q^{56} - 20 q^{57} + 40 q^{59} + 122 q^{61} + 8 q^{62} + 12 q^{63} - 260 q^{64} - 20 q^{65} - 16 q^{66} + 8 q^{67} + 4 q^{68} - 8 q^{69} + 64 q^{70} - 12 q^{71} - 78 q^{73} + 52 q^{74} - 22 q^{75} - 6 q^{76} - 56 q^{77} + 64 q^{78} - 16 q^{79} - 260 q^{81} + 48 q^{82} + 112 q^{83} + 8 q^{84} - 40 q^{85} - 80 q^{86} - 12 q^{87} + 20 q^{88} - 8 q^{89} + 16 q^{90} + 140 q^{91} - 28 q^{93} + 52 q^{94} - 144 q^{95} + 114 q^{97} - 24 q^{98} + 8 q^{99} + O(q^{100}) \)

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

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