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Properties

Label 3822.2.ck
Level $3822$
Weight $2$
Character orbit 3822.ck
Rep. character $\chi_{3822}(209,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1344$
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.ck (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1568\)

Dimensions

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

Total New Old
Modular forms 4752 1344 3408
Cusp forms 4656 1344 3312
Eisenstein series 96 0 96

Trace form

\( 1344 q + 224 q^{4} + 28 q^{6} + 4 q^{7} + 20 q^{9} + O(q^{10}) \) \( 1344 q + 224 q^{4} + 28 q^{6} + 4 q^{7} + 20 q^{9} - 24 q^{15} - 224 q^{16} + 16 q^{21} + 20 q^{22} - 232 q^{25} - 84 q^{27} - 4 q^{28} - 4 q^{30} - 20 q^{36} + 16 q^{37} + 28 q^{40} + 90 q^{42} + 64 q^{43} + 112 q^{45} + 120 q^{46} + 4 q^{49} + 36 q^{51} + 28 q^{55} - 68 q^{57} - 100 q^{58} + 24 q^{60} + 20 q^{63} + 224 q^{64} + 76 q^{70} + 126 q^{75} - 72 q^{79} - 52 q^{81} + 68 q^{84} - 64 q^{85} + 8 q^{88} + 42 q^{90} + 8 q^{91} + 96 q^{93} + 448 q^{99} + O(q^{100}) \)

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

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