Properties

Label 1666.2.a
Level $1666$
Weight $2$
Character orbit 1666.a
Rep. character $\chi_{1666}(1,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $27$
Sturm bound $504$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1666.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(504\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1666))\).

Total New Old
Modular forms 268 56 212
Cusp forms 237 56 181
Eisenstein series 31 0 31

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(10\)
Plus space\(+\)\(23\)
Minus space\(-\)\(33\)

Trace form

\( 56q - 2q^{3} + 56q^{4} - 2q^{5} + 6q^{6} + 60q^{9} + O(q^{10}) \) \( 56q - 2q^{3} + 56q^{4} - 2q^{5} + 6q^{6} + 60q^{9} + 6q^{10} + 2q^{11} - 2q^{12} + 4q^{13} + 56q^{16} + 2q^{17} + 12q^{18} + 16q^{19} - 2q^{20} + 2q^{22} + 8q^{23} + 6q^{24} + 60q^{25} + 4q^{26} - 20q^{27} - 6q^{29} + 4q^{31} - 4q^{33} + 2q^{34} + 60q^{36} - 42q^{37} - 16q^{38} - 20q^{39} + 6q^{40} + 20q^{41} - 36q^{43} + 2q^{44} + 14q^{45} + 8q^{46} - 16q^{47} - 2q^{48} + 20q^{50} - 2q^{51} + 4q^{52} + 12q^{53} + 12q^{54} - 8q^{55} - 16q^{57} + 2q^{58} + 4q^{59} + 26q^{61} + 4q^{62} + 56q^{64} + 4q^{65} + 12q^{66} - 52q^{67} + 2q^{68} - 32q^{69} - 16q^{71} + 12q^{72} + 8q^{73} - 18q^{74} + 18q^{75} + 16q^{76} - 12q^{78} - 32q^{79} - 2q^{80} + 76q^{81} - 12q^{82} - 36q^{83} - 6q^{85} + 12q^{86} + 24q^{87} + 2q^{88} - 16q^{89} + 6q^{90} + 8q^{92} - 48q^{93} + 16q^{94} + 56q^{95} + 6q^{96} + 4q^{97} - 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1666))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 17
1666.2.a.a \(1\) \(13.303\) \(\Q\) None \(-1\) \(-3\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-3q^{3}+q^{4}+2q^{5}+3q^{6}-q^{8}+\cdots\)
1666.2.a.b \(1\) \(13.303\) \(\Q\) None \(-1\) \(-2\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-2q^{3}+q^{4}-4q^{5}+2q^{6}-q^{8}+\cdots\)
1666.2.a.c \(1\) \(13.303\) \(\Q\) None \(-1\) \(-2\) \(3\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+3q^{5}+2q^{6}-q^{8}+\cdots\)
1666.2.a.d \(1\) \(13.303\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
1666.2.a.e \(1\) \(13.303\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-3q^{9}-2q^{10}+\cdots\)
1666.2.a.f \(1\) \(13.303\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
1666.2.a.g \(1\) \(13.303\) \(\Q\) None \(-1\) \(2\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-3q^{5}-2q^{6}-q^{8}+\cdots\)
1666.2.a.h \(1\) \(13.303\) \(\Q\) None \(-1\) \(3\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+3q^{3}+q^{4}-2q^{5}-3q^{6}-q^{8}+\cdots\)
1666.2.a.i \(1\) \(13.303\) \(\Q\) None \(1\) \(-2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots\)
1666.2.a.j \(1\) \(13.303\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots\)
1666.2.a.k \(1\) \(13.303\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots\)
1666.2.a.l \(1\) \(13.303\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
1666.2.a.m \(1\) \(13.303\) \(\Q\) None \(1\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots\)
1666.2.a.n \(1\) \(13.303\) \(\Q\) None \(1\) \(2\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+4q^{5}+2q^{6}+q^{8}+\cdots\)
1666.2.a.o \(2\) \(13.303\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
1666.2.a.p \(2\) \(13.303\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+(-2+\beta )q^{5}-\beta q^{6}+\cdots\)
1666.2.a.q \(2\) \(13.303\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}+(2+\beta )q^{5}-\beta q^{6}+\cdots\)
1666.2.a.r \(2\) \(13.303\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
1666.2.a.s \(2\) \(13.303\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1-\beta )q^{5}+\cdots\)
1666.2.a.t \(3\) \(13.303\) 3.3.404.1 None \(-3\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{2}q^{5}+\cdots\)
1666.2.a.u \(3\) \(13.303\) 3.3.404.1 None \(-3\) \(0\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots\)
1666.2.a.v \(4\) \(13.303\) 4.4.4352.1 None \(-4\) \(0\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1666.2.a.w \(4\) \(13.303\) 4.4.4352.1 None \(-4\) \(0\) \(4\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
1666.2.a.x \(4\) \(13.303\) 4.4.4352.1 None \(4\) \(-4\) \(-8\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
1666.2.a.y \(4\) \(13.303\) 4.4.4352.1 None \(4\) \(4\) \(8\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
1666.2.a.z \(5\) \(13.303\) 5.5.23949216.1 None \(5\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
1666.2.a.ba \(5\) \(13.303\) 5.5.23949216.1 None \(5\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1666))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1666)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(833))\)\(^{\oplus 2}\)