↑

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 $1$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.2.f.a 74.f 37.f $6$ $0.591$ \(\Q(\zeta_{18})\) None 74.2.f.a \(0\) \(-3\) \(3\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-\zeta_{18}-\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
74.2.f.b 74.f 37.f $12$ $0.591$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 74.2.f.b \(0\) \(-3\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{4}-\beta _{7})q^{2}+(-1+\beta _{1}-\beta _{8})q^{3}+\cdots\)

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

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