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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.2.c.a 74.c 37.c $2$ $0.591$ \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
74.2.c.b 74.c 37.c $2$ $0.591$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+2\zeta_{6}q^{3}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
74.2.c.c 74.c 37.c $6$ $0.591$ 6.0.4406832.1 None \(-3\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{3})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\beta _{3}q^{4}+\cdots\)

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

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