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Properties

Label 315.2.bv
Level $315$
Weight $2$
Character orbit 315.bv
Rep. character $\chi_{315}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $176$
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.bv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
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 208 208 0
Cusp forms 176 176 0
Eisenstein series 32 32 0

Trace form

\( 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7} + O(q^{10}) \) \( 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 24 q^{11} + 26 q^{12} - 4 q^{13} - 14 q^{15} - 136 q^{16} + 18 q^{17} - 10 q^{18} - 12 q^{20} - 16 q^{21} + 4 q^{22} - 30 q^{23} + 2 q^{25} - 32 q^{27} - 4 q^{28} + 10 q^{30} - 8 q^{31} - 34 q^{33} + 8 q^{36} - 4 q^{37} - 30 q^{38} + 18 q^{40} - 36 q^{41} + 8 q^{42} - 4 q^{43} + 22 q^{45} + 4 q^{46} + 38 q^{48} + 36 q^{50} - 40 q^{51} + 26 q^{52} + 4 q^{55} + 24 q^{56} + 32 q^{57} + 6 q^{58} + 22 q^{60} + 16 q^{61} + 14 q^{63} + 4 q^{66} - 4 q^{67} + 114 q^{68} + 18 q^{70} - 46 q^{72} - 4 q^{73} + 6 q^{75} - 24 q^{76} - 54 q^{77} + 54 q^{78} - 36 q^{80} - 64 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 120 q^{86} - 28 q^{87} - 6 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} - 38 q^{93} + 192 q^{96} - 4 q^{97} - 12 q^{98} + O(q^{100}) \)

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.bv.a 315.bv 315.av $176$ $2.515$ None \(0\) \(-2\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{12}]$