Properties

Label 804.2.c
Level 804
Weight 2
Character orbit c
Rep. character \(\chi_{804}(671,\cdot)\)
Character field \(\Q\)
Dimension 132
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
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 140 132 8
Cusp forms 132 132 0
Eisenstein series 8 0 8

Trace form

\( 132q - 4q^{4} - 6q^{6} + O(q^{10}) \) \( 132q - 4q^{4} - 6q^{6} + 4q^{10} + 4q^{12} + 12q^{16} + 2q^{18} - 8q^{22} - 24q^{24} - 124q^{25} + 14q^{30} + 32q^{34} + 26q^{36} - 16q^{37} - 12q^{42} - 28q^{46} - 22q^{48} - 140q^{49} - 8q^{52} - 16q^{54} - 16q^{57} - 52q^{58} - 14q^{60} - 16q^{61} - 16q^{64} - 18q^{66} + 16q^{69} - 4q^{70} + 24q^{72} - 8q^{73} - 36q^{76} + 40q^{78} + 16q^{81} + 52q^{82} + 30q^{84} + 32q^{85} - 28q^{88} - 6q^{90} + 32q^{93} - 8q^{96} + 40q^{97} + O(q^{100}) \)

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.c.a \(4\) \(6.420\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}-2q^{4}-\zeta_{8}^{2}q^{5}+\cdots\)
804.2.c.b \(128\) \(6.420\) None \(0\) \(0\) \(0\) \(0\)