Properties

Label 240.4.bb
Level $240$
Weight $4$
Character orbit 240.bb
Rep. character $\chi_{240}(173,\cdot)$
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.bb (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

\( 280 q + 12 q^{4} - 4 q^{6} + O(q^{10}) \) \( 280 q + 12 q^{4} - 4 q^{6} - 36 q^{10} + 52 q^{12} - 4 q^{15} - 140 q^{16} - 224 q^{18} + 24 q^{19} - 4 q^{21} - 252 q^{22} - 108 q^{24} + 172 q^{28} + 632 q^{30} - 16 q^{31} - 4 q^{33} - 924 q^{34} - 260 q^{36} + 216 q^{39} + 1276 q^{40} + 220 q^{42} + 856 q^{43} + 248 q^{45} - 92 q^{46} - 2192 q^{48} - 4 q^{51} - 744 q^{52} - 1104 q^{54} + 108 q^{57} - 332 q^{58} - 1112 q^{60} + 904 q^{61} - 1376 q^{63} - 1596 q^{64} + 1644 q^{66} - 8 q^{67} - 108 q^{69} + 4924 q^{70} + 2272 q^{72} + 1704 q^{75} - 2612 q^{76} - 3652 q^{78} - 8 q^{81} + 1632 q^{82} - 2880 q^{84} - 504 q^{85} - 108 q^{87} - 3620 q^{88} + 964 q^{90} - 8 q^{91} + 420 q^{94} + 1392 q^{96} - 8 q^{97} + 2656 q^{99} + O(q^{100}) \)

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