Properties

Label 574.2.f
Level $574$
Weight $2$
Character orbit 574.f
Rep. character $\chi_{574}(155,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
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.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(i)\)
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 176 44 132
Cusp forms 160 44 116
Eisenstein series 16 0 16

Trace form

\( 44q - 4q^{3} - 44q^{4} + 4q^{6} + O(q^{10}) \) \( 44q - 4q^{3} - 44q^{4} + 4q^{6} + 12q^{11} + 4q^{12} - 32q^{13} + 16q^{15} + 44q^{16} + 4q^{17} + 12q^{18} + 28q^{19} - 20q^{22} + 16q^{23} - 4q^{24} - 68q^{25} + 8q^{26} - 16q^{27} + 24q^{29} - 8q^{30} - 12q^{34} - 8q^{35} - 8q^{37} - 4q^{38} - 8q^{41} + 8q^{42} - 12q^{44} - 64q^{45} + 8q^{47} - 4q^{48} + 88q^{51} + 32q^{52} - 16q^{53} - 16q^{54} - 16q^{55} + 40q^{57} - 16q^{60} + 16q^{63} - 44q^{64} + 8q^{65} - 24q^{66} - 12q^{67} - 4q^{68} - 56q^{69} + 8q^{70} - 24q^{71} - 12q^{72} + 36q^{75} - 28q^{76} + 96q^{78} + 16q^{79} - 20q^{81} - 12q^{82} - 8q^{83} + 8q^{85} + 20q^{88} - 12q^{89} - 16q^{92} - 8q^{93} + 16q^{94} + 4q^{96} + 52q^{97} + 4q^{98} + 20q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
574.2.f.a \(20\) \(4.583\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{14}q^{2}+\beta _{13}q^{3}-q^{4}+\beta _{4}q^{5}+\cdots\)
574.2.f.b \(24\) \(4.583\) None \(0\) \(0\) \(0\) \(0\)

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

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