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Properties

Label 3822.2.q
Level $3822$
Weight $2$
Character orbit 3822.q
Rep. character $\chi_{3822}(881,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $376$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1568\)

Dimensions

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

Total New Old
Modular forms 1632 376 1256
Cusp forms 1504 376 1128
Eisenstein series 128 0 128

Trace form

\( 376 q - 188 q^{4} + 8 q^{9} + O(q^{10}) \) \( 376 q - 188 q^{4} + 8 q^{9} + 24 q^{15} - 188 q^{16} - 392 q^{25} + 20 q^{30} + 8 q^{36} - 84 q^{37} - 44 q^{39} - 4 q^{43} - 24 q^{46} + 72 q^{51} + 376 q^{64} + 72 q^{67} + 56 q^{78} - 176 q^{79} - 72 q^{81} + 192 q^{85} - 72 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3822, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1911, [\chi])\)\(^{\oplus 2}\)