Properties

Label 74.2.f
Level $74$
Weight $2$
Character orbit 74.f
Rep. character $\chi_{74}(7,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $18$
Newform subspaces $2$
Sturm bound $19$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(19\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(74, [\chi])\).

Total New Old
Modular forms 66 18 48
Cusp forms 42 18 24
Eisenstein series 24 0 24

Trace form

\( 18q - 6q^{3} - 3q^{5} + 12q^{7} - 3q^{8} - 6q^{9} + O(q^{10}) \) \( 18q - 6q^{3} - 3q^{5} + 12q^{7} - 3q^{8} - 6q^{9} - 6q^{10} - 6q^{11} - 6q^{12} - 6q^{13} + 6q^{14} - 12q^{15} - 3q^{17} + 6q^{19} - 3q^{20} - 30q^{21} - 36q^{23} + 15q^{25} - 9q^{26} + 6q^{27} - 6q^{28} + 6q^{29} + 24q^{30} + 24q^{31} + 54q^{33} - 3q^{34} - 6q^{35} + 18q^{36} + 6q^{37} + 48q^{38} - 6q^{39} + 18q^{40} - 15q^{41} - 36q^{42} + 48q^{43} - 6q^{44} - 6q^{45} + 18q^{46} + 6q^{47} - 12q^{49} + 18q^{50} + 12q^{52} - 24q^{53} - 36q^{54} - 18q^{55} - 24q^{57} - 21q^{58} - 12q^{59} - 30q^{61} - 36q^{62} + 42q^{63} - 9q^{64} + 3q^{65} - 30q^{67} - 12q^{68} + 30q^{69} - 12q^{70} - 24q^{71} + 18q^{73} + 21q^{74} - 36q^{75} + 6q^{76} + 36q^{77} - 42q^{78} + 18q^{79} - 12q^{80} - 24q^{81} - 24q^{82} - 12q^{84} - 15q^{85} + 12q^{86} + 12q^{87} + 12q^{88} - 48q^{89} - 21q^{90} - 42q^{91} + 6q^{92} + 48q^{93} - 24q^{94} + 36q^{95} + 60q^{98} - 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(74, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
74.2.f.a \(6\) \(0.591\) \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(3\) \(6\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-\zeta_{18}-\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
74.2.f.b \(12\) \(0.591\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(-6\) \(6\) \(q+(\beta _{4}-\beta _{7})q^{2}+(-1+\beta _{1}-\beta _{8})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(74, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)