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Properties

Label 3822.2.bs
Level $3822$
Weight $2$
Character orbit 3822.bs
Rep. character $\chi_{3822}(547,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $672$
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.bs (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(1568\)

Dimensions

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

Total New Old
Modular forms 4752 672 4080
Cusp forms 4656 672 3984
Eisenstein series 96 0 96

Trace form

\( 672 q - 112 q^{4} - 16 q^{5} - 4 q^{6} - 12 q^{7} - 112 q^{9} + O(q^{10}) \) \( 672 q - 112 q^{4} - 16 q^{5} - 4 q^{6} - 12 q^{7} - 112 q^{9} - 8 q^{10} + 40 q^{11} - 4 q^{13} - 4 q^{14} + 20 q^{15} - 112 q^{16} + 32 q^{17} + 48 q^{19} + 40 q^{20} + 12 q^{22} - 16 q^{23} - 4 q^{24} - 136 q^{25} - 12 q^{28} - 40 q^{29} - 40 q^{31} - 16 q^{33} - 32 q^{34} - 48 q^{35} - 112 q^{36} - 16 q^{37} - 12 q^{38} + 20 q^{40} + 80 q^{41} + 44 q^{42} - 48 q^{43} - 16 q^{44} + 40 q^{45} + 64 q^{47} - 8 q^{49} - 32 q^{50} + 40 q^{51} - 4 q^{52} + 72 q^{53} - 4 q^{54} + 20 q^{55} - 4 q^{56} + 60 q^{58} + 16 q^{59} + 20 q^{60} - 40 q^{61} + 20 q^{62} - 12 q^{63} - 112 q^{64} - 32 q^{67} - 24 q^{68} - 32 q^{69} + 4 q^{70} - 32 q^{71} - 40 q^{73} - 32 q^{74} - 8 q^{76} - 80 q^{77} - 72 q^{79} - 16 q^{80} - 112 q^{81} - 48 q^{82} + 184 q^{83} - 64 q^{85} + 20 q^{87} + 12 q^{88} + 168 q^{89} - 8 q^{90} - 8 q^{91} - 16 q^{92} - 8 q^{94} - 16 q^{95} - 4 q^{96} + 24 q^{97} - 48 q^{98} - 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3822, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1911, [\chi])\)\(^{\oplus 2}\)