Properties

Label 68.2.a
Level 68
Weight 2
Character orbit a
Rep. character \(\chi_{68}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) = \( 68 = 2^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 68.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(68))\).

Total New Old
Modular forms 12 2 10
Cusp forms 7 2 5
Eisenstein series 5 0 5

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

\(2\)\(17\)FrickeDim.
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2q + 2q^{3} - 2q^{7} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{3} - 2q^{7} + 2q^{9} - 6q^{11} + 4q^{13} - 12q^{15} - 2q^{17} + 4q^{19} - 8q^{21} - 6q^{23} + 14q^{25} + 8q^{27} - 2q^{31} + 12q^{35} + 16q^{37} + 16q^{39} - 12q^{41} + 4q^{43} - 24q^{45} - 6q^{49} - 2q^{51} + 12q^{53} - 12q^{55} - 8q^{57} + 12q^{59} - 8q^{61} - 14q^{63} - 24q^{65} + 16q^{67} - 6q^{71} + 4q^{73} + 14q^{75} - 14q^{79} + 2q^{81} - 12q^{83} + 12q^{87} + 12q^{89} - 16q^{91} + 16q^{93} + 24q^{95} + 4q^{97} + 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(68))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 17
68.2.a.a \(2\) \(0.543\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(+\) \(q+(1+\beta )q^{3}-2\beta q^{5}+(-1-\beta )q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(68))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(68)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 2}\)