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Properties

Label 240.4.t
Level $240$
Weight $4$
Character orbit 240.t
Rep. character $\chi_{240}(59,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
Newform subspaces $2$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(192\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(240, [\chi])\).

Total New Old
Modular forms 296 296 0
Cusp forms 280 280 0
Eisenstein series 16 16 0

Trace form

\( 280 q - 8 q^{4} - 4 q^{6} + O(q^{10}) \) \( 280 q - 8 q^{4} - 4 q^{6} - 4 q^{10} + 124 q^{16} - 32 q^{19} + 104 q^{21} + 364 q^{24} - 832 q^{30} - 132 q^{34} + 692 q^{36} - 8 q^{39} + 920 q^{40} - 252 q^{45} - 156 q^{46} - 11384 q^{49} - 112 q^{51} - 1488 q^{54} - 296 q^{55} + 2872 q^{60} - 920 q^{61} + 1504 q^{64} + 4072 q^{66} - 112 q^{69} - 1440 q^{70} + 1596 q^{75} + 7492 q^{76} - 8 q^{81} - 2080 q^{84} - 504 q^{85} + 4440 q^{90} + 2736 q^{91} - 4036 q^{94} + 4776 q^{96} - 5576 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.4.t.a 240.t 240.t $8$ $14.160$ 8.0.3317760000.5 \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-\beta _{1}-\beta _{6})q^{2}+(2\beta _{1}+\beta _{6})q^{3}+(6\beta _{3}+\cdots)q^{4}+\cdots\)
240.4.t.b 240.t 240.t $272$ $14.160$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$