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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 127
2667.2.a.a \(1\) \(21.296\) \(\Q\) None \(-2\) \(1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
2667.2.a.b \(1\) \(21.296\) \(\Q\) None \(-1\) \(-1\) \(4\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}-q^{4}+4q^{5}+q^{6}-q^{7}+\cdots\)
2667.2.a.c \(1\) \(21.296\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
2667.2.a.d \(1\) \(21.296\) \(\Q\) None \(0\) \(1\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}+3q^{5}+q^{7}+q^{9}+6q^{11}+\cdots\)
2667.2.a.e \(1\) \(21.296\) \(\Q\) None \(2\) \(1\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots\)
2667.2.a.f \(2\) \(21.296\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-3\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}+(-1-\beta )q^{5}-q^{7}+q^{9}+\cdots\)
2667.2.a.g \(2\) \(21.296\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+q^{3}-\beta q^{5}+\beta q^{6}+q^{7}-2\beta q^{8}+\cdots\)
2667.2.a.h \(2\) \(21.296\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+4q^{4}+\beta q^{5}+\beta q^{6}+\cdots\)
2667.2.a.i \(2\) \(21.296\) \(\Q(\sqrt{17}) \) None \(1\) \(-2\) \(3\) \(-2\) \(+\) \(+\) \(-\) \(q+\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
2667.2.a.j \(7\) \(21.296\) 7.7.118870813.1 None \(-2\) \(7\) \(-8\) \(7\) \(-\) \(-\) \(+\) \(q+\beta _{4}q^{2}+q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2667.2.a.k \(11\) \(21.296\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-2\) \(11\) \(1\) \(-11\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
2667.2.a.l \(13\) \(21.296\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(4\) \(-13\) \(12\) \(13\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{10}+\cdots)q^{5}+\cdots\)
2667.2.a.m \(14\) \(21.296\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-5\) \(-14\) \(-4\) \(-14\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
2667.2.a.n \(16\) \(21.296\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(16\) \(5\) \(-16\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
2667.2.a.o \(16\) \(21.296\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(5\) \(-16\) \(-1\) \(-16\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots\)
2667.2.a.p \(18\) \(21.296\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-6\) \(-18\) \(-10\) \(18\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{12}+\cdots)q^{5}+\cdots\)
2667.2.a.q \(19\) \(21.296\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(4\) \(19\) \(5\) \(19\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)

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

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