Properties

Label 2667.2.a
Level $2667$
Weight $2$
Character orbit 2667.a
Rep. character $\chi_{2667}(1,\cdot)$
Character field $\Q$
Dimension $127$
Newform subspaces $17$
Sturm bound $682$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 2667 = 3 \cdot 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2667.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(682\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2667))\).

Total New Old
Modular forms 344 127 217
Cusp forms 337 127 210
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.

\(3\)\(7\)\(127\)FrickeDim
\(+\)\(+\)\(+\)$+$\(14\)
\(+\)\(+\)\(-\)$-$\(19\)
\(+\)\(-\)\(+\)$-$\(13\)
\(+\)\(-\)\(-\)$+$\(18\)
\(-\)\(+\)\(+\)$-$\(17\)
\(-\)\(+\)\(-\)$+$\(14\)
\(-\)\(-\)\(+\)$+$\(10\)
\(-\)\(-\)\(-\)$-$\(22\)
Plus space\(+\)\(56\)
Minus space\(-\)\(71\)

Trace form

\( 127 q + q^{2} - q^{3} + 133 q^{4} + 10 q^{5} + 5 q^{6} - q^{7} - 3 q^{8} + 127 q^{9} + O(q^{10}) \) \( 127 q + q^{2} - q^{3} + 133 q^{4} + 10 q^{5} + 5 q^{6} - q^{7} - 3 q^{8} + 127 q^{9} - 2 q^{10} - 12 q^{11} - 7 q^{12} + 2 q^{13} - 3 q^{14} + 2 q^{15} + 133 q^{16} + 14 q^{17} + q^{18} - 4 q^{19} + 38 q^{20} + 3 q^{21} + 20 q^{22} - 8 q^{23} + 9 q^{24} + 145 q^{25} + 38 q^{26} - q^{27} - 7 q^{28} + 2 q^{29} - 2 q^{30} + 16 q^{31} + 25 q^{32} - 12 q^{33} + 22 q^{34} - 6 q^{35} + 133 q^{36} - 6 q^{37} - 8 q^{38} + 2 q^{39} - 2 q^{40} + 30 q^{41} + q^{42} - 28 q^{43} - 64 q^{44} + 10 q^{45} - 8 q^{46} - 24 q^{47} - 31 q^{48} + 127 q^{49} - 25 q^{50} + 6 q^{51} - 38 q^{52} + 10 q^{53} + 5 q^{54} - 32 q^{55} - 15 q^{56} - 12 q^{57} - 34 q^{58} - 36 q^{59} + 6 q^{60} + 10 q^{61} + 28 q^{62} - q^{63} + 157 q^{64} + 36 q^{65} - 20 q^{66} - 52 q^{67} - 6 q^{68} + 16 q^{69} + 22 q^{70} - 32 q^{71} - 3 q^{72} + 54 q^{73} + 58 q^{74} - 15 q^{75} + 52 q^{76} - 12 q^{77} + 30 q^{78} + 32 q^{79} + 46 q^{80} + 127 q^{81} - 30 q^{82} + 28 q^{83} + 5 q^{84} + 4 q^{85} - 20 q^{86} - 22 q^{87} + 32 q^{88} + 38 q^{89} - 2 q^{90} - 6 q^{91} - 32 q^{92} + 8 q^{93} - 8 q^{94} + 73 q^{96} - 2 q^{97} + q^{98} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2667))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 127
2667.2.a.a 2667.a 1.a $1$ $21.296$ \(\Q\) None \(-2\) \(1\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
2667.2.a.b 2667.a 1.a $1$ $21.296$ \(\Q\) None \(-1\) \(-1\) \(4\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+4q^{5}+q^{6}-q^{7}+\cdots\)
2667.2.a.c 2667.a 1.a $1$ $21.296$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
2667.2.a.d 2667.a 1.a $1$ $21.296$ \(\Q\) None \(0\) \(1\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+3q^{5}+q^{7}+q^{9}+6q^{11}+\cdots\)
2667.2.a.e 2667.a 1.a $1$ $21.296$ \(\Q\) None \(2\) \(1\) \(3\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots\)
2667.2.a.f 2667.a 1.a $2$ $21.296$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-3\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+(-1-\beta )q^{5}-q^{7}+q^{9}+\cdots\)
2667.2.a.g 2667.a 1.a $2$ $21.296$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}-\beta q^{5}+\beta q^{6}+q^{7}-2\beta q^{8}+\cdots\)
2667.2.a.h 2667.a 1.a $2$ $21.296$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+4q^{4}+\beta q^{5}+\beta q^{6}+\cdots\)
2667.2.a.i 2667.a 1.a $2$ $21.296$ \(\Q(\sqrt{17}) \) None \(1\) \(-2\) \(3\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
2667.2.a.j 2667.a 1.a $7$ $21.296$ 7.7.118870813.1 None \(-2\) \(7\) \(-8\) \(7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2667.2.a.k 2667.a 1.a $11$ $21.296$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-2\) \(11\) \(1\) \(-11\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
2667.2.a.l 2667.a 1.a $13$ $21.296$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(4\) \(-13\) \(12\) \(13\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{10}+\cdots)q^{5}+\cdots\)
2667.2.a.m 2667.a 1.a $14$ $21.296$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-5\) \(-14\) \(-4\) \(-14\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
2667.2.a.n 2667.a 1.a $16$ $21.296$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(16\) \(5\) \(-16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
2667.2.a.o 2667.a 1.a $16$ $21.296$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(5\) \(-16\) \(-1\) \(-16\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots\)
2667.2.a.p 2667.a 1.a $18$ $21.296$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-6\) \(-18\) \(-10\) \(18\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{12}+\cdots)q^{5}+\cdots\)
2667.2.a.q 2667.a 1.a $19$ $21.296$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(4\) \(19\) \(5\) \(19\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2667))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2667)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(127))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(381))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(889))\)\(^{\oplus 2}\)