Properties

Label 315.2.bx
Level 315
Weight 2
Character orbit bx
Rep. character \(\chi_{315}(2,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 176
Newforms 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.bx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Newforms: \( 1 \)
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

\(176q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 24q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(176q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 24q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 22q^{12} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 14q^{15} \) \(\mathstrut +\mathstrut 68q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut -\mathstrut 10q^{18} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut +\mathstrut 20q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 32q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 20q^{30} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 90q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 8q^{36} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 36q^{40} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 68q^{45} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 38q^{48} \) \(\mathstrut +\mathstrut 36q^{50} \) \(\mathstrut +\mathstrut 20q^{51} \) \(\mathstrut -\mathstrut 52q^{52} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 96q^{56} \) \(\mathstrut +\mathstrut 32q^{57} \) \(\mathstrut -\mathstrut 12q^{58} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut +\mathstrut 14q^{63} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 92q^{66} \) \(\mathstrut +\mathstrut 2q^{67} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 46q^{72} \) \(\mathstrut -\mathstrut 4q^{73} \) \(\mathstrut +\mathstrut 54q^{75} \) \(\mathstrut -\mathstrut 24q^{76} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 36q^{80} \) \(\mathstrut +\mathstrut 20q^{81} \) \(\mathstrut -\mathstrut 8q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 28q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 24q^{90} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 72q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 66q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut 12q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
315.2.bx.a \(176\) \(2.515\) None \(-6\) \(-2\) \(0\) \(-2\)