Properties

Label 74.2.c
Level $74$
Weight $2$
Character orbit 74.c
Rep. character $\chi_{74}(47,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $3$
Sturm bound $19$
Trace bound $3$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 22 10 12
Cusp forms 14 10 4
Eisenstein series 8 0 8

Trace form

\( 10q - q^{2} - 5q^{4} - 3q^{5} + 4q^{7} + 2q^{8} - 9q^{9} + O(q^{10}) \) \( 10q - q^{2} - 5q^{4} - 3q^{5} + 4q^{7} + 2q^{8} - 9q^{9} - 2q^{10} - 2q^{13} + 8q^{14} + 4q^{15} - 5q^{16} - 3q^{17} - 5q^{18} - 12q^{19} - 3q^{20} + 8q^{21} - 8q^{22} + 16q^{23} - 20q^{25} + 20q^{26} - 24q^{27} + 4q^{28} - 18q^{29} - 12q^{30} + 32q^{31} - q^{32} - 4q^{33} + 9q^{34} + 16q^{35} + 18q^{36} - q^{37} + 8q^{38} + 16q^{39} + q^{40} + q^{41} + 24q^{42} - 8q^{43} + 70q^{45} - 8q^{46} - 40q^{47} + 3q^{49} - 20q^{50} - 64q^{51} - 2q^{52} - 10q^{53} + 12q^{54} - 12q^{55} - 4q^{56} + 20q^{57} - 3q^{58} - 12q^{59} - 8q^{60} - 3q^{61} + 8q^{62} + 16q^{63} + 10q^{64} - 14q^{65} - 56q^{66} + 20q^{67} + 6q^{68} + 28q^{69} - 8q^{70} + 24q^{71} - 5q^{72} - 20q^{73} + 18q^{74} + 56q^{75} - 12q^{76} - 36q^{77} - 16q^{78} - 16q^{79} + 6q^{80} + 11q^{81} - 26q^{82} - 12q^{83} - 16q^{84} - 6q^{85} - 20q^{86} + 8q^{87} + 16q^{88} + q^{89} - 31q^{90} + 8q^{91} - 8q^{92} - 36q^{93} + 12q^{94} + 32q^{95} + 6q^{97} + 7q^{98} - 48q^{99} + O(q^{100}) \)

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.c.a \(2\) \(0.591\) \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
74.2.c.b \(2\) \(0.591\) \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-3\) \(4\) \(q+(1-\zeta_{6})q^{2}+2\zeta_{6}q^{3}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
74.2.c.c \(6\) \(0.591\) 6.0.4406832.1 None \(-3\) \(0\) \(-1\) \(0\) \(q+(-1-\beta _{3})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\beta _{3}q^{4}+\cdots\)

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

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