Properties

Label 668.2.a
Level 668
Weight 2
Character orbit a
Rep. character \(\chi_{668}(1,\cdot)\)
Character field \(\Q\)
Dimension 14
Newforms 3
Sturm bound 168
Trace bound 1

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Defining parameters

Level: \( N \) = \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 668.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(668))\).

Total New Old
Modular forms 87 14 73
Cusp forms 82 14 68
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.

\(2\)\(167\)FrickeDim.
\(-\)\(+\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(7\)
Minus space\(-\)\(7\)

Trace form

\( 14q + 2q^{5} + 14q^{9} + O(q^{10}) \) \( 14q + 2q^{5} + 14q^{9} - 2q^{11} - 4q^{13} - 14q^{15} - 2q^{17} - 2q^{19} - 14q^{23} + 6q^{25} - 2q^{29} + 2q^{31} - 16q^{33} + 2q^{35} - 10q^{37} - 6q^{39} - 4q^{41} - 4q^{43} + 2q^{45} - 2q^{47} + 30q^{49} + 2q^{51} + 6q^{55} + 4q^{57} - 6q^{59} - 2q^{61} - 14q^{63} - 22q^{65} - 12q^{67} + 14q^{69} + 8q^{71} + 18q^{73} + 26q^{75} + 2q^{79} + 6q^{81} + 22q^{83} - 34q^{85} - 2q^{87} - 14q^{89} + 6q^{91} - 32q^{93} + 8q^{95} - 44q^{97} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(668))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 167
668.2.a.a \(2\) \(5.334\) \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(-6\) \(3\) \(-\) \(+\) \(q+\beta q^{3}-3q^{5}+(1+\beta )q^{7}+\beta q^{9}+(4+\cdots)q^{13}+\cdots\)
668.2.a.b \(5\) \(5.334\) 5.5.826865.1 None \(0\) \(3\) \(10\) \(9\) \(-\) \(+\) \(q+(1-\beta _{2})q^{3}+2q^{5}+(2-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
668.2.a.c \(7\) \(5.334\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-4\) \(-2\) \(-12\) \(-\) \(-\) \(q+(-1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(668))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(668)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 2}\)