Properties

Label 3822.2.do
Level $3822$
Weight $2$
Character orbit 3822.do
Rep. character $\chi_{3822}(269,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $3144$
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.do (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1911 \)
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 3144 6360
Cusp forms 9312 3144 6168
Eisenstein series 192 0 192

Trace form

\( 3144 q + 524 q^{4} - 10 q^{7} + O(q^{10}) \) \( 3144 q + 524 q^{4} - 10 q^{7} + 2 q^{13} - 524 q^{16} + 4 q^{18} - 18 q^{19} + 8 q^{21} + 266 q^{25} + 10 q^{28} + 6 q^{30} - 12 q^{31} - 72 q^{33} + 30 q^{37} + 22 q^{39} - 86 q^{42} + 6 q^{43} - 140 q^{45} + 66 q^{49} - 6 q^{51} + 40 q^{52} + 24 q^{55} + 216 q^{61} - 2 q^{63} + 524 q^{64} + 24 q^{66} + 52 q^{67} - 86 q^{69} - 4 q^{72} + 54 q^{73} - 84 q^{75} + 18 q^{76} + 16 q^{78} + 36 q^{79} - 16 q^{81} + 24 q^{82} - 8 q^{84} + 80 q^{85} - 56 q^{87} + 42 q^{90} + 232 q^{91} - 148 q^{93} - 200 q^{94} - 66 q^{97} + O(q^{100}) \)

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

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