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 $2$

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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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 37
74.2.a.a \(2\) \(0.591\) \(\Q(\sqrt{13}) \) None \(-2\) \(3\) \(-1\) \(2\) \(+\) \(-\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
74.2.a.b \(2\) \(0.591\) \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(1\) \(-2\) \(-\) \(+\) \(q+q^{2}-\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots\)

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

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