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Properties

Label 315.2.cc
Level $315$
Weight $2$
Character orbit 315.cc
Rep. character $\chi_{315}(92,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $144$
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.cc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 208 144 64
Cusp forms 176 144 32
Eisenstein series 32 0 32

Trace form

\( 144 q + 4 q^{3} + O(q^{10}) \) \( 144 q + 4 q^{3} - 12 q^{11} - 16 q^{12} + 16 q^{15} + 72 q^{16} - 64 q^{18} - 48 q^{20} - 4 q^{21} - 24 q^{23} - 12 q^{25} - 32 q^{27} - 20 q^{30} - 60 q^{32} - 16 q^{33} - 16 q^{36} - 24 q^{37} + 72 q^{38} + 48 q^{41} - 40 q^{42} + 40 q^{45} - 48 q^{46} + 12 q^{47} + 104 q^{48} - 76 q^{51} - 24 q^{55} - 4 q^{57} - 92 q^{60} + 8 q^{63} - 72 q^{65} - 80 q^{66} - 12 q^{67} - 64 q^{72} - 108 q^{75} - 24 q^{76} + 72 q^{78} + 32 q^{81} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 144 q^{86} + 116 q^{87} - 48 q^{88} + 252 q^{90} + 24 q^{91} + 156 q^{92} - 44 q^{93} + 120 q^{95} - 96 q^{96} - 60 q^{97} + O(q^{100}) \)

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.cc.a 315.cc 45.l $144$ $2.515$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)