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Properties

Label 403.2.bt
Level $403$
Weight $2$
Character orbit 403.bt
Rep. character $\chi_{403}(82,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $280$
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.bt (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 312 312 0
Cusp forms 280 280 0
Eisenstein series 32 32 0

Trace form

\( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9} + O(q^{10}) \) \( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9} + 3 q^{10} - 8 q^{12} - 6 q^{13} + 4 q^{14} - 45 q^{15} + 23 q^{16} + 27 q^{17} + 45 q^{18} - 15 q^{19} - 12 q^{20} - 76 q^{21} + 41 q^{22} - 10 q^{23} - 33 q^{24} + 96 q^{25} + 9 q^{26} - 24 q^{27} - 32 q^{28} + 13 q^{29} + 36 q^{30} + 2 q^{31} - 141 q^{32} - 93 q^{33} - 9 q^{34} - 43 q^{35} - 194 q^{36} + 3 q^{37} - 49 q^{38} + 50 q^{39} - 75 q^{40} - 15 q^{41} + 17 q^{42} + 33 q^{43} + 18 q^{44} - 15 q^{45} - 9 q^{46} - 59 q^{48} + 3 q^{49} + 36 q^{50} + 47 q^{51} - 56 q^{52} + 12 q^{53} - 33 q^{54} - 5 q^{55} - 50 q^{56} - 105 q^{57} - 3 q^{58} - 15 q^{59} + 90 q^{60} - 57 q^{61} - 72 q^{62} + 201 q^{63} + 13 q^{64} - 43 q^{65} + 22 q^{66} - 71 q^{68} - 7 q^{69} - 42 q^{71} + 90 q^{72} + 9 q^{73} - 113 q^{74} + 45 q^{75} + 14 q^{76} - 24 q^{77} + 61 q^{78} + 54 q^{79} + 30 q^{80} + 106 q^{81} + 16 q^{82} + 54 q^{83} + 60 q^{84} + 18 q^{85} + 84 q^{86} + 42 q^{87} - 98 q^{88} - 99 q^{89} + 11 q^{90} + 60 q^{91} + 266 q^{92} - 104 q^{93} + 33 q^{94} - 120 q^{95} + 204 q^{96} - 50 q^{97} - 15 q^{98} - 168 q^{99} + O(q^{100}) \)

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.bt.a 403.bt 403.at $280$ $3.218$ None \(-9\) \(-3\) \(0\) \(-15\) $\mathrm{SU}(2)[C_{30}]$