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Properties

Label 3822.2.o
Level $3822$
Weight $2$
Character orbit 3822.o
Rep. character $\chi_{3822}(2449,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
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.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Sturm bound: \(1568\)

Dimensions

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

Total New Old
Modular forms 1632 192 1440
Cusp forms 1504 192 1312
Eisenstein series 128 0 128

Trace form

\( 192 q - 192 q^{9} + O(q^{10}) \) \( 192 q - 192 q^{9} + 16 q^{11} - 192 q^{16} + 16 q^{22} - 16 q^{29} + 80 q^{37} + 16 q^{39} + 16 q^{44} + 48 q^{50} - 48 q^{53} - 32 q^{57} - 64 q^{58} + 96 q^{65} - 48 q^{67} - 112 q^{71} + 128 q^{74} + 16 q^{78} + 64 q^{79} + 192 q^{81} - 192 q^{85} + 80 q^{86} + 32 q^{92} - 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3822, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 2}\)