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Properties

Label 352.2.bc
Level $352$
Weight $2$
Character orbit 352.bc
Rep. character $\chi_{352}(19,\cdot)$
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.bc (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

\( 736 q - 20 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} - 12 q^{9} + O(q^{10}) \) \( 736 q - 20 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} - 12 q^{9} - 16 q^{11} - 20 q^{13} - 28 q^{14} - 24 q^{15} - 52 q^{16} - 120 q^{18} - 20 q^{19} + 4 q^{20} - 4 q^{22} - 48 q^{23} - 20 q^{24} - 12 q^{25} + 48 q^{26} - 12 q^{27} - 20 q^{28} - 20 q^{29} - 20 q^{30} - 32 q^{33} + 24 q^{34} - 20 q^{35} - 12 q^{36} - 12 q^{37} - 12 q^{38} - 20 q^{39} - 20 q^{40} - 20 q^{41} - 52 q^{42} + 24 q^{44} - 8 q^{45} - 20 q^{46} - 24 q^{47} - 12 q^{48} - 20 q^{50} - 20 q^{51} - 20 q^{52} - 60 q^{53} + 16 q^{55} - 248 q^{56} - 20 q^{57} - 12 q^{58} + 20 q^{59} + 68 q^{60} - 20 q^{61} - 20 q^{62} + 132 q^{64} - 8 q^{66} - 112 q^{67} - 20 q^{68} - 12 q^{69} + 36 q^{70} + 20 q^{71} - 320 q^{72} - 20 q^{73} - 20 q^{74} + 124 q^{75} - 32 q^{77} - 80 q^{78} - 40 q^{79} + 124 q^{80} + 28 q^{82} - 20 q^{83} - 20 q^{84} - 20 q^{85} - 116 q^{86} - 20 q^{88} - 32 q^{89} - 20 q^{90} - 156 q^{91} + 148 q^{92} - 36 q^{93} - 160 q^{94} - 20 q^{96} - 24 q^{97} - 68 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bc.a 352.bc 352.ac $736$ $2.811$ None 352.2.bc.a \(-20\) \(-12\) \(-12\) \(-20\) $\mathrm{SU}(2)[C_{40}]$