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Properties

Label 415.2.j
Level $415$
Weight $2$
Character orbit 415.j
Rep. character $\chi_{415}(4,\cdot)$
Character field $\Q(\zeta_{82})$
Dimension $1600$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 415 = 5 \cdot 83 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 415.j (of order \(82\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 415 \)
Character field: \(\Q(\zeta_{82})\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(415, [\chi])\).

Total New Old
Modular forms 1760 1760 0
Cusp forms 1600 1600 0
Eisenstein series 160 160 0

Trace form

\( 1600 q - 44 q^{4} - 37 q^{5} - 82 q^{6} - 50 q^{9} + O(q^{10}) \) \( 1600 q - 44 q^{4} - 37 q^{5} - 82 q^{6} - 50 q^{9} - 31 q^{10} - 78 q^{11} - 90 q^{14} - 49 q^{15} - 116 q^{16} - 78 q^{19} - 47 q^{20} - 70 q^{21} - 66 q^{24} - 53 q^{25} - 98 q^{26} - 90 q^{29} - 53 q^{30} - 74 q^{31} - 106 q^{34} - 61 q^{35} - 68 q^{36} - 86 q^{39} - 35 q^{40} - 74 q^{41} - 78 q^{44} - 35 q^{45} - 102 q^{46} - 22 q^{49} - 41 q^{50} - 50 q^{51} - 114 q^{54} - 59 q^{55} - 86 q^{56} - 102 q^{59} + 9 q^{60} - 70 q^{61} - 92 q^{64} - 33 q^{65} - 118 q^{66} - 102 q^{69} + 111 q^{70} - 86 q^{71} - 10 q^{74} + 262 q^{75} - 34 q^{76} - 22 q^{79} + 367 q^{80} - 130 q^{81} - 172 q^{84} + 78 q^{85} - 26 q^{86} - 78 q^{89} + 267 q^{90} - 138 q^{91} - 130 q^{94} + 82 q^{95} - 118 q^{96} - 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(415, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
415.2.j.a 415.j 415.j $1600$ $3.314$ None 415.2.j.a \(0\) \(0\) \(-37\) \(0\) $\mathrm{SU}(2)[C_{82}]$