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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23 29
667.2.a.a \(10\) \(5.326\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-9\) \(-10\) \(1\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
667.2.a.b \(12\) \(5.326\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(-3\) \(-16\) \(-7\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1-\beta _{4}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots\)
667.2.a.c \(13\) \(5.326\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(4\) \(3\) \(16\) \(1\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
667.2.a.d \(16\) \(5.326\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(3\) \(5\) \(16\) \(1\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)

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

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