Properties

Label 667.2.a
Level $667$
Weight $2$
Character orbit 667.a
Rep. character $\chi_{667}(1,\cdot)$
Character field $\Q$
Dimension $51$
Newform subspaces $4$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 667.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(667))\).

Total New Old
Modular forms 62 51 11
Cusp forms 59 51 8
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.

\(23\)\(29\)FrickeDim
\(+\)\(+\)$+$\(12\)
\(+\)\(-\)$-$\(13\)
\(-\)\(+\)$-$\(16\)
\(-\)\(-\)$+$\(10\)
Plus space\(+\)\(22\)
Minus space\(-\)\(29\)

Trace form

\( 51 q + q^{2} - 4 q^{3} + 53 q^{4} + 6 q^{5} + 8 q^{6} - 4 q^{7} - 3 q^{8} + 47 q^{9} + O(q^{10}) \) \( 51 q + q^{2} - 4 q^{3} + 53 q^{4} + 6 q^{5} + 8 q^{6} - 4 q^{7} - 3 q^{8} + 47 q^{9} - 10 q^{10} + 8 q^{11} - 32 q^{12} - 6 q^{13} - 24 q^{14} + 24 q^{15} + 37 q^{16} + 6 q^{17} + 9 q^{18} - 12 q^{19} + 14 q^{20} + 8 q^{21} - 4 q^{22} + q^{23} - 16 q^{24} + 73 q^{25} - 18 q^{26} - 16 q^{27} - 8 q^{28} - 5 q^{29} - 52 q^{30} - 12 q^{31} - 55 q^{32} - 24 q^{33} - 6 q^{34} - 20 q^{35} + 21 q^{36} + 10 q^{37} + 12 q^{38} - 4 q^{39} + 18 q^{40} - 6 q^{41} - 32 q^{42} - 36 q^{43} + 4 q^{44} + 14 q^{45} - q^{46} - 8 q^{47} - 4 q^{48} + 55 q^{49} - 13 q^{50} - 24 q^{51} - 6 q^{52} + 18 q^{53} - 40 q^{54} + 4 q^{55} - 48 q^{56} - 32 q^{57} + q^{58} - 16 q^{59} + 72 q^{60} + 18 q^{61} + 40 q^{62} + 61 q^{64} + 44 q^{65} - 24 q^{66} - 20 q^{67} + 34 q^{68} - 4 q^{69} - 4 q^{71} + 25 q^{72} - 46 q^{73} - 42 q^{74} - 8 q^{75} - 28 q^{76} + 4 q^{77} + 20 q^{78} - 34 q^{80} + 59 q^{81} + 14 q^{82} - 4 q^{83} + 56 q^{85} - 16 q^{86} - 8 q^{87} - 40 q^{88} + 2 q^{89} - 22 q^{90} - 48 q^{91} + 7 q^{92} + 44 q^{93} + 32 q^{94} + 8 q^{96} - 6 q^{97} - 23 q^{98} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(667))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 23 29
667.2.a.a 667.a 1.a $10$ $5.326$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-9\) \(-10\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
667.2.a.b 667.a 1.a $12$ $5.326$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(-3\) \(-16\) \(-7\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1-\beta _{4}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots\)
667.2.a.c 667.a 1.a $13$ $5.326$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(4\) \(3\) \(16\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
667.2.a.d 667.a 1.a $16$ $5.326$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(3\) \(5\) \(16\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(667))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(667)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)