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Properties

Label 574.2.s
Level $574$
Weight $2$
Character orbit 574.s
Rep. character $\chi_{574}(37,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $224$
Newform subspaces $2$
Sturm bound $168$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 574 = 2 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 574.s (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(574, [\chi])\).

Total New Old
Modular forms 704 224 480
Cusp forms 640 224 416
Eisenstein series 64 0 64

Trace form

\( 224 q + 28 q^{4} + 4 q^{5} + 8 q^{6} - 116 q^{9} + O(q^{10}) \) \( 224 q + 28 q^{4} + 4 q^{5} + 8 q^{6} - 116 q^{9} + 4 q^{10} - 4 q^{11} + 36 q^{14} + 24 q^{15} + 28 q^{16} - 12 q^{17} - 4 q^{19} - 8 q^{20} - 46 q^{21} + 24 q^{22} + 6 q^{23} + 6 q^{24} + 44 q^{25} - 4 q^{26} - 24 q^{27} - 52 q^{29} + 14 q^{30} - 8 q^{31} + 2 q^{33} + 16 q^{34} + 60 q^{35} - 48 q^{36} + 38 q^{37} - 20 q^{39} - 16 q^{40} - 44 q^{41} - 48 q^{42} + 8 q^{43} + 16 q^{44} + 28 q^{45} + 10 q^{46} - 44 q^{47} - 28 q^{49} - 96 q^{50} + 26 q^{51} + 62 q^{53} - 24 q^{54} + 56 q^{55} + 16 q^{56} + 32 q^{57} + 16 q^{58} + 28 q^{59} + 18 q^{60} - 18 q^{61} - 8 q^{62} - 72 q^{63} - 56 q^{64} + 28 q^{65} - 8 q^{66} + 4 q^{67} - 12 q^{68} + 36 q^{69} + 64 q^{70} - 36 q^{71} - 44 q^{73} - 36 q^{74} - 42 q^{75} + 8 q^{76} + 100 q^{77} + 104 q^{78} - 20 q^{79} + 4 q^{80} - 176 q^{81} - 44 q^{82} + 96 q^{83} + 2 q^{84} - 48 q^{85} + 6 q^{86} - 40 q^{87} - 12 q^{88} + 42 q^{89} - 72 q^{90} - 52 q^{91} + 8 q^{92} - 28 q^{93} + 4 q^{94} + 66 q^{95} - 4 q^{96} + 24 q^{97} - 24 q^{98} + 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(574, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
574.2.s.a 574.s 287.s $112$ $4.583$ None \(-14\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{15}]$
574.2.s.b 574.s 287.s $112$ $4.583$ None \(14\) \(-2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(574, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(574, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)