Properties

Label 240.2.bb
Level $240$
Weight $2$
Character orbit 240.bb
Rep. character $\chi_{240}(173,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.bb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(240, [\chi])\).

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

Trace form

\( 88q - 4q^{4} - 4q^{6} + O(q^{10}) \) \( 88q - 4q^{4} - 4q^{6} - 12q^{10} + 4q^{12} - 4q^{15} - 12q^{16} + 16q^{18} - 8q^{19} - 4q^{21} - 20q^{22} - 12q^{24} - 36q^{28} - 16q^{30} - 16q^{31} - 4q^{33} + 28q^{34} - 20q^{36} + 24q^{39} - 4q^{40} - 20q^{42} - 40q^{43} + 8q^{45} - 36q^{46} + 16q^{48} - 4q^{51} + 24q^{52} - 24q^{54} + 12q^{57} + 44q^{58} - 56q^{60} - 24q^{61} - 32q^{63} - 28q^{64} + 12q^{66} - 8q^{67} - 12q^{69} - 28q^{70} + 64q^{72} - 24q^{75} - 36q^{76} + 20q^{78} - 8q^{81} - 48q^{82} + 48q^{84} - 24q^{85} - 12q^{87} + 60q^{88} + 76q^{90} - 8q^{91} - 20q^{94} + 48q^{96} - 8q^{97} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
240.2.bb.a \(88\) \(1.916\) None \(0\) \(0\) \(0\) \(0\)