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Properties

Label 471.2.q
Level $471$
Weight $2$
Character orbit 471.q
Rep. character $\chi_{471}(19,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $648$
Newform subspaces $2$
Sturm bound $105$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.q (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 157 \)
Character field: \(\Q(\zeta_{39})\)
Newform subspaces: \( 2 \)
Sturm bound: \(105\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(471, [\chi])\).

Total New Old
Modular forms 1320 648 672
Cusp forms 1224 648 576
Eisenstein series 96 0 96

Trace form

\( 648 q - 4 q^{2} + q^{3} - 56 q^{4} + 6 q^{5} + 27 q^{9} + O(q^{10}) \) \( 648 q - 4 q^{2} + q^{3} - 56 q^{4} + 6 q^{5} + 27 q^{9} - 2 q^{10} - 6 q^{11} - 28 q^{12} - 57 q^{13} - 24 q^{14} - 2 q^{15} - 52 q^{16} - 10 q^{17} + 2 q^{18} + q^{19} + 6 q^{20} + 4 q^{21} + 16 q^{22} + 8 q^{23} + 41 q^{25} - 10 q^{26} - 2 q^{27} - 120 q^{28} + 92 q^{29} + 4 q^{30} - 36 q^{31} - 44 q^{32} - 24 q^{33} - 106 q^{34} + 128 q^{35} + 28 q^{36} - 45 q^{37} - 102 q^{38} - 10 q^{39} + 122 q^{40} - 188 q^{41} + 5 q^{43} - 12 q^{45} + 72 q^{46} + 14 q^{47} - 12 q^{48} - 106 q^{49} - 114 q^{50} + 4 q^{51} - 44 q^{52} - 72 q^{53} - 90 q^{55} - 48 q^{56} - 5 q^{57} + 52 q^{58} - 52 q^{59} - 8 q^{60} - 74 q^{61} - 204 q^{62} + 52 q^{63} - 16 q^{64} + 88 q^{65} - 64 q^{66} - 78 q^{67} + 314 q^{68} - 2 q^{69} + 10 q^{70} - 14 q^{71} - 36 q^{73} - 58 q^{74} + 2 q^{75} - 2 q^{76} - 50 q^{77} - 102 q^{78} + 88 q^{79} + 142 q^{80} + 27 q^{81} - 132 q^{83} + 20 q^{84} - 88 q^{85} - 152 q^{86} - 16 q^{87} + 34 q^{88} + 22 q^{89} + 4 q^{90} + 228 q^{91} - 192 q^{92} - 24 q^{93} - 48 q^{94} - 4 q^{95} + 250 q^{96} - 202 q^{97} - 148 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(471, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
471.2.q.a 471.q 157.i $312$ $3.761$ None \(-2\) \(-13\) \(4\) \(4\) $\mathrm{SU}(2)[C_{39}]$
471.2.q.b 471.q 157.i $336$ $3.761$ None \(-2\) \(14\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{39}]$

Decomposition of \(S_{2}^{\mathrm{old}}(471, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(471, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(157, [\chi])\)\(^{\oplus 2}\)