Properties

Label 240.2.t
Level $240$
Weight $2$
Character orbit 240.t
Rep. character $\chi_{240}(59,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

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

\( 88q - 8q^{4} - 4q^{6} + O(q^{10}) \) \( 88q - 8q^{4} - 4q^{6} - 4q^{10} - 4q^{16} + 8q^{21} - 20q^{24} + 8q^{30} - 60q^{34} - 28q^{36} - 8q^{39} - 8q^{40} - 12q^{45} - 52q^{46} - 56q^{49} - 16q^{51} + 24q^{54} - 40q^{55} + 40q^{60} + 8q^{61} - 32q^{64} - 56q^{66} - 16q^{69} + 48q^{70} - 36q^{75} - 76q^{76} - 8q^{81} + 128q^{84} - 24q^{85} + 72q^{90} + 48q^{91} + 52q^{94} - 24q^{96} - 8q^{99} + O(q^{100}) \)

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.t.a \(8\) \(1.916\) 8.0.3317760000.5 \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+\beta _{2}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
240.2.t.b \(80\) \(1.916\) None \(0\) \(0\) \(0\) \(0\)