Properties

Label 574.2.e
Level $574$
Weight $2$
Character orbit 574.e
Rep. character $\chi_{574}(165,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $56$
Newform subspaces $8$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 574 = 2 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 574.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(168\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 176 56 120
Cusp forms 160 56 104
Eisenstein series 16 0 16

Trace form

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

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.e.a \(2\) \(4.583\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(2\) \(5\) \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
574.2.e.b \(2\) \(4.583\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
574.2.e.c \(2\) \(4.583\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(1\) \(-1\) \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
574.2.e.d \(4\) \(4.583\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(-1\) \(1\) \(-10\) \(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}-\beta _{1}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
574.2.e.e \(6\) \(4.583\) 6.0.309123.1 None \(-3\) \(3\) \(-4\) \(-4\) \(q+(-1+\beta _{4})q^{2}+\beta _{4}q^{3}-\beta _{4}q^{4}+(-1+\cdots)q^{5}+\cdots\)
574.2.e.f \(8\) \(4.583\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(-4\) \(-3\) \(5\) \(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
574.2.e.g \(12\) \(4.583\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(-1\) \(0\) \(-1\) \(q-\beta _{8}q^{2}+\beta _{2}q^{3}+(-1-\beta _{8})q^{4}+\beta _{10}q^{5}+\cdots\)
574.2.e.h \(20\) \(4.583\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-10\) \(1\) \(-2\) \(1\) \(q+\beta _{10}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{10}+\cdots)q^{4}+\cdots\)

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

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