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Properties

Label 240.4.s
Level $240$
Weight $4$
Character orbit 240.s
Rep. character $\chi_{240}(61,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 96 200
Cusp forms 280 96 184
Eisenstein series 16 0 16

Trace form

\( 96 q + 40 q^{4} + O(q^{10}) \) \( 96 q + 40 q^{4} - 60 q^{10} + 80 q^{11} + 488 q^{14} - 120 q^{15} + 252 q^{16} + 72 q^{18} - 24 q^{19} - 80 q^{20} - 976 q^{22} - 228 q^{24} + 688 q^{28} - 800 q^{29} + 1240 q^{32} + 1348 q^{34} - 108 q^{36} - 32 q^{37} - 440 q^{38} - 1616 q^{43} + 232 q^{44} + 2852 q^{46} - 4704 q^{49} - 200 q^{50} - 744 q^{51} - 792 q^{52} - 1504 q^{53} - 108 q^{54} - 3024 q^{56} - 1856 q^{58} + 1376 q^{59} + 912 q^{61} + 2928 q^{62} + 1008 q^{63} + 1648 q^{64} + 1368 q^{66} + 816 q^{67} + 6104 q^{68} + 528 q^{69} + 2480 q^{70} + 1224 q^{72} + 3424 q^{74} + 3212 q^{76} - 3808 q^{77} - 3528 q^{78} - 2832 q^{79} - 7776 q^{81} - 2280 q^{82} - 3600 q^{84} + 240 q^{85} - 1008 q^{86} + 8648 q^{88} + 5296 q^{91} - 5048 q^{92} - 6884 q^{94} - 600 q^{96} - 9232 q^{98} + 720 q^{99} + O(q^{100}) \)

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.s.a 240.s 16.e $44$ $14.160$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
240.4.s.b 240.s 16.e $52$ $14.160$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)