Properties

Label 74.2.a
Level $74$
Weight $2$
Character orbit 74.a
Rep. character $\chi_{74}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $19$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(19\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(74))\).

Total New Old
Modular forms 11 4 7
Cusp forms 8 4 4
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(37\)FrickeDim.
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(0\)
Minus space\(-\)\(4\)

Trace form

\( 4 q + 2 q^{3} + 4 q^{4} - 4 q^{6} + 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} + 4 q^{4} - 4 q^{6} + 2 q^{9} + 2 q^{10} - 6 q^{11} + 2 q^{12} - 4 q^{14} - 16 q^{15} + 4 q^{16} - 12 q^{17} - 8 q^{18} + 4 q^{19} - 4 q^{21} - 4 q^{22} - 4 q^{23} - 4 q^{24} + 10 q^{25} + 2 q^{26} + 20 q^{27} + 20 q^{31} - 8 q^{33} + 12 q^{34} - 4 q^{35} + 2 q^{36} - 4 q^{38} + 12 q^{39} + 2 q^{40} + 26 q^{41} + 16 q^{42} - 12 q^{43} - 6 q^{44} - 16 q^{45} + 2 q^{46} + 4 q^{47} + 2 q^{48} + 12 q^{49} + 16 q^{50} - 8 q^{51} - 20 q^{53} - 16 q^{54} + 12 q^{55} - 4 q^{56} - 4 q^{57} - 6 q^{58} - 16 q^{60} + 16 q^{61} + 14 q^{62} - 36 q^{63} + 4 q^{64} - 28 q^{65} + 8 q^{66} + 2 q^{67} - 12 q^{68} + 8 q^{69} - 28 q^{70} - 8 q^{72} - 18 q^{73} - 4 q^{74} - 12 q^{75} + 4 q^{76} + 12 q^{77} + 2 q^{78} - 4 q^{79} + 36 q^{81} + 8 q^{82} - 4 q^{84} - 24 q^{85} + 4 q^{87} - 4 q^{88} - 16 q^{89} + 28 q^{90} - 4 q^{92} - 8 q^{93} + 28 q^{95} - 4 q^{96} + 4 q^{97} - 16 q^{98} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(74))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 37
74.2.a.a 74.a 1.a $2$ $0.591$ \(\Q(\sqrt{13}) \) None \(-2\) \(3\) \(-1\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
74.2.a.b 74.a 1.a $2$ $0.591$ \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(1\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(74))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(74)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)