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Properties

Label 403.2.bs
Level $403$
Weight $2$
Character orbit 403.bs
Rep. character $\chi_{403}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $288$
Newform subspaces $1$
Sturm bound $74$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.bs (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(74\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(403, [\chi])\).

Total New Old
Modular forms 320 320 0
Cusp forms 288 288 0
Eisenstein series 32 32 0

Trace form

\( 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9} + O(q^{10}) \) \( 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9} + 3 q^{10} - 18 q^{11} - 46 q^{12} - q^{13} - 32 q^{14} + 18 q^{15} + 21 q^{16} - 15 q^{17} - 15 q^{19} + 51 q^{20} - 10 q^{22} - 4 q^{23} - 51 q^{24} - 296 q^{25} - 6 q^{26} - 52 q^{27} + 21 q^{28} + q^{29} + 60 q^{30} + 138 q^{32} + 69 q^{33} - 10 q^{35} + 128 q^{36} - 18 q^{37} + 32 q^{38} - 14 q^{39} + 60 q^{40} - 15 q^{41} - 49 q^{42} - 36 q^{43} + 6 q^{45} - 69 q^{46} + 21 q^{48} - 23 q^{49} + 117 q^{50} + 8 q^{51} + 26 q^{52} - 48 q^{53} + 75 q^{54} + 46 q^{55} - 98 q^{56} - 21 q^{58} - 105 q^{59} - 74 q^{61} - 3 q^{62} - 90 q^{63} + 90 q^{64} + 89 q^{65} - 8 q^{66} + 6 q^{67} - 182 q^{68} + 29 q^{69} + 3 q^{71} - 183 q^{72} - 53 q^{74} - 38 q^{75} + 144 q^{76} - 128 q^{78} - 72 q^{79} - 72 q^{80} + 11 q^{81} - 11 q^{82} - 33 q^{84} + 72 q^{85} - 18 q^{87} - 14 q^{88} + 81 q^{89} - 34 q^{90} - 48 q^{91} + 8 q^{92} + 72 q^{93} - 6 q^{94} + 141 q^{97} + 96 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
403.2.bs.a 403.bs 403.as $288$ $3.218$ None \(-9\) \(-1\) \(0\) \(-15\) $\mathrm{SU}(2)[C_{30}]$