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Properties

Label 315.2.bq
Level $315$
Weight $2$
Character orbit 315.bq
Rep. character $\chi_{315}(164,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bq (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6} + O(q^{10}) \) \( 88 q + 76 q^{4} - 3 q^{5} - 12 q^{6} - 6 q^{10} - 12 q^{11} - 12 q^{14} - 6 q^{15} + 52 q^{16} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 48 q^{24} + q^{25} - 12 q^{26} + 6 q^{29} + 33 q^{30} - 12 q^{34} - 36 q^{36} + 12 q^{39} - 30 q^{40} + 6 q^{41} - 84 q^{44} + 21 q^{45} - 18 q^{46} - 8 q^{49} + 30 q^{50} - 24 q^{51} - 60 q^{54} - 78 q^{56} - 12 q^{59} - 45 q^{60} - 8 q^{64} - 24 q^{66} + 60 q^{69} + 15 q^{70} - 30 q^{74} - 48 q^{75} - 48 q^{76} - 16 q^{79} - 69 q^{80} + 36 q^{81} - 90 q^{84} - 7 q^{85} - 12 q^{86} + 72 q^{89} + 33 q^{90} + 20 q^{91} - 60 q^{96} + 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
315.2.bq.a 315.bq 315.aq $88$ $2.515$ None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$