Properties

Label 304.3.j
Level $304$
Weight $3$
Character orbit 304.j
Rep. character $\chi_{304}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $156$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 304.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(304, [\chi])\).

Total New Old
Modular forms 164 164 0
Cusp forms 156 156 0
Eisenstein series 8 8 0

Trace form

\( 156q - 4q^{4} - 4q^{5} - 4q^{6} + O(q^{10}) \) \( 156q - 4q^{4} - 4q^{5} - 4q^{6} - 4q^{11} - 60q^{16} - 8q^{17} + 30q^{19} + 80q^{20} + 52q^{24} + 144q^{26} - 184q^{30} + 192q^{35} - 36q^{36} - 184q^{38} - 60q^{42} - 4q^{43} - 12q^{44} + 132q^{45} - 8q^{47} - 932q^{49} + 160q^{54} + 80q^{58} - 68q^{61} - 372q^{62} + 384q^{63} + 128q^{64} + 100q^{66} - 576q^{68} + 88q^{74} + 580q^{76} + 192q^{77} - 80q^{80} - 1124q^{81} - 100q^{82} + 156q^{83} + 216q^{85} - 72q^{92} + 32q^{93} + 380q^{95} + 1200q^{96} + 484q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
304.3.j.a \(156\) \(8.283\) None \(0\) \(0\) \(-4\) \(0\)