Properties

Label 70.2.a
Level $70$
Weight $2$
Character orbit 70.a
Rep. character $\chi_{70}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 70.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(70))\).

Total New Old
Modular forms 16 1 15
Cusp forms 9 1 8
Eisenstein series 7 0 7

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

\(2\)\(5\)\(7\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - 3q^{9} - q^{10} + 4q^{11} - 6q^{13} - q^{14} + q^{16} + 2q^{17} - 3q^{18} - q^{20} + 4q^{22} + q^{25} - 6q^{26} - q^{28} + 6q^{29} + 8q^{31} + q^{32} + 2q^{34} + q^{35} - 3q^{36} - 10q^{37} - q^{40} + 2q^{41} + 4q^{43} + 4q^{44} + 3q^{45} + 8q^{47} + q^{49} + q^{50} - 6q^{52} - 2q^{53} - 4q^{55} - q^{56} + 6q^{58} - 8q^{59} - 14q^{61} + 8q^{62} + 3q^{63} + q^{64} + 6q^{65} - 12q^{67} + 2q^{68} + q^{70} - 16q^{71} - 3q^{72} + 2q^{73} - 10q^{74} - 4q^{77} - 8q^{79} - q^{80} + 9q^{81} + 2q^{82} + 8q^{83} - 2q^{85} + 4q^{86} + 4q^{88} + 10q^{89} + 3q^{90} + 6q^{91} + 8q^{94} + 2q^{97} + q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(70))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7
70.2.a.a \(1\) \(0.559\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(70))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(70)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)