Properties

Label 352.2.bf
Level $352$
Weight $2$
Character orbit 352.bf
Rep. character $\chi_{352}(5,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $736$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 352 = 2^{5} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 352.bf (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 352 \)
Character field: \(\Q(\zeta_{40})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(352, [\chi])\).

Total New Old
Modular forms 800 800 0
Cusp forms 736 736 0
Eisenstein series 64 64 0

Trace form

\( 736 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} + O(q^{10}) \) \( 736 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 12 q^{8} - 12 q^{9} - 32 q^{10} - 16 q^{11} - 64 q^{12} - 12 q^{13} - 28 q^{14} - 52 q^{16} + 48 q^{18} - 12 q^{19} - 28 q^{20} - 32 q^{21} - 28 q^{22} - 48 q^{23} - 12 q^{24} - 12 q^{25} - 72 q^{26} - 12 q^{27} - 12 q^{28} - 12 q^{29} - 28 q^{30} - 24 q^{31} + 8 q^{32} - 32 q^{33} - 8 q^{34} - 12 q^{35} - 12 q^{36} - 12 q^{37} - 12 q^{38} - 12 q^{39} + 28 q^{40} - 12 q^{41} - 52 q^{42} - 48 q^{43} - 56 q^{44} - 56 q^{45} - 76 q^{46} - 12 q^{48} - 12 q^{50} - 36 q^{51} - 28 q^{52} + 36 q^{53} - 120 q^{54} + 16 q^{55} + 184 q^{56} - 12 q^{57} - 12 q^{58} + 20 q^{59} + 4 q^{60} - 12 q^{61} + 4 q^{62} + 56 q^{63} - 156 q^{64} - 64 q^{65} + 8 q^{66} + 48 q^{67} - 100 q^{68} - 12 q^{69} + 36 q^{70} + 20 q^{71} + 168 q^{72} - 12 q^{73} - 44 q^{74} - 148 q^{75} - 32 q^{76} - 32 q^{77} + 16 q^{78} - 148 q^{80} - 52 q^{82} - 12 q^{83} + 100 q^{84} - 52 q^{85} + 92 q^{86} - 32 q^{87} - 20 q^{88} - 32 q^{89} - 180 q^{90} + 132 q^{91} + 132 q^{92} + 12 q^{93} + 8 q^{94} - 152 q^{95} - 76 q^{96} - 24 q^{97} - 48 q^{98} - 68 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(352, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
352.2.bf.a 352.bf 352.af $736$ $2.811$ None 352.2.bf.a \(-12\) \(-12\) \(-12\) \(-12\) $\mathrm{SU}(2)[C_{40}]$