Properties

Label 804.2.s
Level 804
Weight 2
Character orbit s
Rep. character \(\chi_{804}(5,\cdot)\)
Character field \(\Q(\zeta_{22})\)
Dimension 220
Newform subspaces 2
Sturm bound 272
Trace bound 1

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Defining parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.s (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(272\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(804, [\chi])\).

Total New Old
Modular forms 1420 220 1200
Cusp forms 1300 220 1080
Eisenstein series 120 0 120

Trace form

\( 220q - 4q^{9} + O(q^{10}) \) \( 220q - 4q^{9} + 2q^{15} + 22q^{19} - 22q^{21} - 10q^{25} - 44q^{31} - 5q^{33} - 20q^{37} + 54q^{39} - 22q^{43} - 22q^{45} - 6q^{49} + 36q^{55} + 176q^{61} + 30q^{67} + 64q^{73} - 165q^{75} + 24q^{81} - 66q^{87} + 28q^{91} + 48q^{93} - 55q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(804, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
804.2.s.a \(20\) \(6.420\) \(\Q(\zeta_{33})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{33}^{13}q^{3}+(-2\zeta_{33}^{7}-2\zeta_{33}^{8}+\cdots)q^{7}+\cdots\)
804.2.s.b \(200\) \(6.420\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(804, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(804, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(402, [\chi])\)\(^{\oplus 2}\)