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Properties

Label 304.2.m
Level $304$
Weight $2$
Character orbit 304.m
Rep. character $\chi_{304}(75,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $76$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(304, [\chi])\).

Total New Old
Modular forms 84 84 0
Cusp forms 76 76 0
Eisenstein series 8 8 0

Trace form

\( 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7} + O(q^{10}) \) \( 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7} - 4 q^{11} + 4 q^{16} - 8 q^{17} + 6 q^{19} - 32 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{26} - 40 q^{30} + 44 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{42} - 4 q^{43} - 76 q^{44} + 4 q^{45} + 44 q^{49} + 96 q^{54} - 8 q^{55} + 24 q^{58} + 28 q^{61} + 20 q^{62} - 64 q^{64} + 12 q^{66} - 80 q^{74} + 12 q^{76} - 32 q^{77} - 16 q^{80} - 52 q^{81} + 68 q^{82} + 36 q^{83} - 56 q^{85} - 120 q^{87} - 8 q^{92} - 16 q^{93} + 48 q^{96} + 76 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
304.2.m.a 304.m 304.m $76$ $2.427$ None \(0\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$