↑

Properties

Label 3822.2.dq
Level $3822$
Weight $2$
Character orbit 3822.dq
Rep. character $\chi_{3822}(131,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2688$
Sturm bound $1568$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3822.dq (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
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 2688 6816
Cusp forms 9312 2688 6624
Eisenstein series 192 0 192

Trace form

\( 2688 q - 224 q^{4} - 28 q^{6} - 4 q^{7} - 32 q^{9} + O(q^{10}) \) \( 2688 q - 224 q^{4} - 28 q^{6} - 4 q^{7} - 32 q^{9} - 12 q^{10} + 24 q^{15} + 224 q^{16} + 8 q^{21} - 20 q^{22} + 12 q^{24} + 220 q^{25} + 84 q^{27} + 4 q^{28} - 2 q^{30} + 12 q^{31} + 20 q^{36} + 8 q^{37} + 44 q^{40} - 108 q^{42} - 64 q^{43} - 112 q^{45} + 312 q^{46} + 164 q^{49} + 18 q^{51} + 644 q^{55} + 68 q^{57} + 328 q^{58} + 12 q^{60} - 72 q^{61} - 56 q^{63} + 448 q^{64} - 48 q^{66} + 8 q^{70} + 96 q^{73} - 138 q^{75} - 36 q^{79} + 16 q^{81} - 68 q^{84} + 64 q^{85} + 12 q^{87} + 4 q^{88} - 42 q^{90} + 16 q^{91} + 300 q^{93} + 12 q^{96} - 448 q^{99} + O(q^{100}) \)

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

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