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Properties

Label 240.4.bf
Level $240$
Weight $4$
Character orbit 240.bf
Rep. character $\chi_{240}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $280$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 240.bf (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

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

\( 280 q - 4 q^{3} - 12 q^{4} - 4 q^{6} + O(q^{10}) \) \( 280 q - 4 q^{3} - 12 q^{4} - 4 q^{6} + 28 q^{10} - 56 q^{12} - 8 q^{13} - 4 q^{15} - 140 q^{16} + 252 q^{18} - 24 q^{19} - 4 q^{21} - 188 q^{22} + 108 q^{24} - 4 q^{27} - 692 q^{28} + 524 q^{30} - 16 q^{31} - 4 q^{33} + 924 q^{34} - 260 q^{36} - 8 q^{37} - 216 q^{39} + 276 q^{40} + 640 q^{42} + 248 q^{45} - 92 q^{46} - 256 q^{48} - 4 q^{51} - 1136 q^{52} + 1104 q^{54} - 108 q^{57} + 2340 q^{58} - 1076 q^{60} + 904 q^{61} - 1376 q^{63} + 1596 q^{64} + 1644 q^{66} + 108 q^{69} + 1692 q^{70} - 1608 q^{72} + 1596 q^{75} - 2612 q^{76} - 2172 q^{78} - 8 q^{81} + 1776 q^{82} + 2880 q^{84} + 496 q^{85} + 108 q^{87} - 6132 q^{88} - 2024 q^{90} - 8 q^{91} - 112 q^{93} - 420 q^{94} + 1392 q^{96} - 8 q^{97} - 2656 q^{99} + O(q^{100}) \)

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.bf.a 240.bf 240.af $280$ $14.160$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$