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Properties

Label 574.2.u
Level $574$
Weight $2$
Character orbit 574.u
Rep. character $\chi_{574}(43,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $176$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 574 = 2 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 574.u (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 704 176 528
Cusp forms 640 176 464
Eisenstein series 64 0 64

Trace form

\( 176 q + 4 q^{3} + 44 q^{4} + 16 q^{6} + O(q^{10}) \) \( 176 q + 4 q^{3} + 44 q^{4} + 16 q^{6} - 12 q^{11} - 4 q^{12} + 32 q^{13} + 64 q^{15} - 44 q^{16} - 4 q^{17} - 12 q^{18} + 32 q^{19} + 20 q^{22} + 24 q^{23} + 4 q^{24} + 68 q^{25} - 8 q^{26} + 16 q^{27} - 24 q^{29} + 8 q^{30} - 40 q^{31} + 12 q^{34} + 8 q^{35} - 20 q^{36} + 8 q^{37} - 36 q^{38} - 160 q^{39} - 32 q^{41} + 32 q^{42} + 12 q^{44} - 96 q^{45} - 40 q^{46} + 32 q^{47} - 16 q^{48} - 8 q^{51} + 8 q^{52} - 24 q^{53} + 16 q^{54} + 96 q^{55} + 16 q^{60} - 16 q^{63} + 44 q^{64} - 8 q^{65} + 24 q^{66} - 48 q^{67} + 24 q^{68} + 136 q^{69} - 8 q^{70} - 56 q^{71} + 12 q^{72} + 104 q^{75} + 28 q^{76} + 104 q^{78} + 64 q^{79} - 360 q^{81} + 12 q^{82} + 8 q^{83} - 168 q^{85} + 40 q^{86} + 80 q^{87} + 20 q^{88} + 12 q^{89} + 16 q^{92} + 8 q^{93} - 16 q^{94} + 80 q^{95} - 4 q^{96} + 68 q^{97} - 4 q^{98} - 80 q^{99} + O(q^{100}) \)

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.u.a 574.u 41.g $80$ $4.583$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$
574.2.u.b 574.u 41.g $96$ $4.583$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

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

\( S_{2}^{\mathrm{old}}(574, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)