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Properties

Label 403.2.bl
Level $403$
Weight $2$
Character orbit 403.bl
Rep. character $\chi_{403}(16,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $288$
Newform subspaces $2$
Sturm bound $74$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.bl (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

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

\( 288 q - 3 q^{2} - 5 q^{3} + 33 q^{4} - 32 q^{5} - 10 q^{6} - 5 q^{7} - 2 q^{8} + 31 q^{9} + O(q^{10}) \) \( 288 q - 3 q^{2} - 5 q^{3} + 33 q^{4} - 32 q^{5} - 10 q^{6} - 5 q^{7} - 2 q^{8} + 31 q^{9} - 9 q^{10} - 6 q^{11} + 14 q^{12} - 5 q^{13} - 48 q^{14} - 12 q^{15} + 45 q^{16} - 3 q^{17} + 6 q^{18} - q^{19} + 15 q^{20} + 38 q^{21} - 34 q^{22} - 18 q^{23} + 43 q^{24} + 232 q^{25} - 6 q^{26} - 68 q^{27} + 3 q^{28} - 23 q^{29} - 36 q^{30} - 60 q^{31} - 26 q^{32} - 25 q^{33} - 136 q^{34} - 28 q^{35} - 152 q^{36} - 26 q^{37} + 16 q^{38} + 18 q^{39} - 116 q^{40} + 13 q^{41} + 31 q^{42} - 28 q^{43} + 12 q^{44} - 52 q^{45} - 15 q^{46} - 20 q^{47} - 11 q^{48} + 45 q^{49} - 21 q^{50} - 104 q^{51} + 62 q^{52} + 16 q^{53} + 49 q^{54} - 40 q^{55} - 78 q^{56} + 140 q^{57} + 31 q^{58} - 19 q^{59} - 52 q^{60} + 34 q^{61} + 3 q^{62} - 122 q^{63} - 102 q^{64} + 17 q^{65} + 16 q^{66} + 6 q^{67} + 86 q^{68} - 67 q^{69} - 22 q^{70} + 41 q^{71} + 47 q^{72} - 56 q^{73} - 9 q^{74} - 4 q^{75} - 34 q^{76} + 40 q^{77} - 72 q^{78} + 80 q^{79} - 114 q^{80} - 29 q^{81} + 45 q^{82} - 134 q^{83} + 81 q^{84} - 54 q^{85} + 212 q^{86} - 38 q^{87} + 82 q^{88} + 21 q^{89} - 26 q^{90} + 46 q^{91} - 336 q^{92} - 30 q^{93} - 18 q^{94} + 34 q^{95} + 186 q^{96} + 13 q^{97} + 88 q^{98} - 60 q^{99} + O(q^{100}) \)

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.bl.a 403.bl 403.al $8$ $3.218$ \(\Q(\zeta_{15})\) None \(-4\) \(-5\) \(-24\) \(-3\) $\mathrm{SU}(2)[C_{15}]$ \(q+(-2+\zeta_{15}+\zeta_{15}^{2}-2\zeta_{15}^{3}+2\zeta_{15}^{4}+\cdots)q^{2}+\cdots\)
403.2.bl.b 403.bl 403.al $280$ $3.218$ None \(1\) \(0\) \(-8\) \(-2\) $\mathrm{SU}(2)[C_{15}]$