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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.2.t.a 240.t 240.t $8$ $1.916$ 8.0.3317760000.5 \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+\beta _{2}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
240.2.t.b 240.t 240.t $80$ $1.916$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$