Properties

Label 241.2.s
Level $241$
Weight $2$
Character orbit 241.s
Rep. character $\chi_{241}(3,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $640$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 241.s (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{120})\)
Newform subspaces: \( 1 \)
Sturm bound: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(241, [\chi])\).

Total New Old
Modular forms 704 704 0
Cusp forms 640 640 0
Eisenstein series 64 64 0

Trace form

\( 640 q - 32 q^{2} - 32 q^{3} - 24 q^{4} - 32 q^{5} - 40 q^{6} - 48 q^{7} - 64 q^{8} - 4 q^{9} + O(q^{10}) \) \( 640 q - 32 q^{2} - 32 q^{3} - 24 q^{4} - 32 q^{5} - 40 q^{6} - 48 q^{7} - 64 q^{8} - 4 q^{9} - 44 q^{10} - 32 q^{11} - 76 q^{12} - 32 q^{13} - 96 q^{14} - 80 q^{15} + 360 q^{16} + 44 q^{17} - 48 q^{18} - 44 q^{19} - 104 q^{20} - 40 q^{21} - 56 q^{22} - 60 q^{23} - 108 q^{24} - 40 q^{25} - 60 q^{26} - 44 q^{27} - 72 q^{28} - 16 q^{29} - 84 q^{30} + 176 q^{31} - 104 q^{32} - 20 q^{33} + 12 q^{34} + 32 q^{35} + 256 q^{36} - 4 q^{37} + 20 q^{38} - 8 q^{39} - 120 q^{40} - 20 q^{41} + 24 q^{42} - 40 q^{43} - 4 q^{44} - 12 q^{45} + 40 q^{46} - 48 q^{47} - 264 q^{48} + 116 q^{49} + 356 q^{50} - 96 q^{51} - 152 q^{52} - 8 q^{53} - 28 q^{54} - 76 q^{55} - 40 q^{56} - 112 q^{57} - 16 q^{58} - 60 q^{59} - 96 q^{60} - 48 q^{61} + 28 q^{62} + 72 q^{63} + 228 q^{65} + 108 q^{66} - 12 q^{67} - 48 q^{68} + 188 q^{69} - 68 q^{70} - 40 q^{71} - 388 q^{72} - 100 q^{73} - 224 q^{74} - 120 q^{75} - 60 q^{76} - 200 q^{78} - 40 q^{79} + 148 q^{80} + 88 q^{81} - 16 q^{82} + 56 q^{83} + 304 q^{84} + 20 q^{85} - 132 q^{86} - 80 q^{87} - 164 q^{88} + 24 q^{89} + 92 q^{90} + 88 q^{91} + 188 q^{92} + 16 q^{93} + 12 q^{94} + 272 q^{95} + 168 q^{96} + 152 q^{97} - 104 q^{98} + 252 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(241, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
241.2.s.a 241.s 241.s $640$ $1.924$ None \(-32\) \(-32\) \(-32\) \(-48\) $\mathrm{SU}(2)[C_{120}]$