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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(70))\) 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 5 7
70.2.a.a 70.a 1.a $1$ $0.559$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)

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

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