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Properties

Label 308.2.be
Level $308$
Weight $2$
Character orbit 308.be
Rep. character $\chi_{308}(3,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $352$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 308.be (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 308 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(308, [\chi])\).

Total New Old
Modular forms 416 416 0
Cusp forms 352 352 0
Eisenstein series 64 64 0

Trace form

\( 352 q - q^{2} - 5 q^{4} - 18 q^{5} - 16 q^{8} + 30 q^{9} + O(q^{10}) \) \( 352 q - q^{2} - 5 q^{4} - 18 q^{5} - 16 q^{8} + 30 q^{9} - 24 q^{10} - 24 q^{12} - 10 q^{14} - 17 q^{16} - 18 q^{17} - 20 q^{18} - 44 q^{21} + 44 q^{22} - 81 q^{24} - 42 q^{25} - 21 q^{26} + 14 q^{28} - 56 q^{29} + q^{30} - 16 q^{32} - 36 q^{33} + 30 q^{36} - 30 q^{37} - 39 q^{38} + 21 q^{40} + 86 q^{42} + 22 q^{44} - 84 q^{45} - 46 q^{46} - 28 q^{49} - 22 q^{50} - 69 q^{52} + 26 q^{53} + 36 q^{54} - 48 q^{57} + 6 q^{58} - 89 q^{60} + 6 q^{61} - 104 q^{64} - 28 q^{65} - 39 q^{66} - 75 q^{68} + 95 q^{70} + 8 q^{72} - 18 q^{73} - 91 q^{74} + 10 q^{77} - 44 q^{78} - 9 q^{80} + 18 q^{81} + 51 q^{82} + 17 q^{84} + 16 q^{85} - 60 q^{86} - 21 q^{88} - 48 q^{89} + 38 q^{92} - 70 q^{93} + 99 q^{94} - 135 q^{96} + 56 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(308, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
308.2.be.a 308.be 308.ae $352$ $2.459$ None \(-1\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{30}]$