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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7 17
1666.2.a.a 1666.a 1.a $1$ $13.303$ \(\Q\) None \(-1\) \(-3\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}+2q^{5}+3q^{6}-q^{8}+\cdots\)
1666.2.a.b 1666.a 1.a $1$ $13.303$ \(\Q\) None \(-1\) \(-2\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-4q^{5}+2q^{6}-q^{8}+\cdots\)
1666.2.a.c 1666.a 1.a $1$ $13.303$ \(\Q\) None \(-1\) \(-2\) \(3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+3q^{5}+2q^{6}-q^{8}+\cdots\)
1666.2.a.d 1666.a 1.a $1$ $13.303$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
1666.2.a.e 1666.a 1.a $1$ $13.303$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-3q^{9}-2q^{10}+\cdots\)
1666.2.a.f 1666.a 1.a $1$ $13.303$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
1666.2.a.g 1666.a 1.a $1$ $13.303$ \(\Q\) None \(-1\) \(2\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-3q^{5}-2q^{6}-q^{8}+\cdots\)
1666.2.a.h 1666.a 1.a $1$ $13.303$ \(\Q\) None \(-1\) \(3\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-2q^{5}-3q^{6}-q^{8}+\cdots\)
1666.2.a.i 1666.a 1.a $1$ $13.303$ \(\Q\) None \(1\) \(-2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots\)
1666.2.a.j 1666.a 1.a $1$ $13.303$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots\)
1666.2.a.k 1666.a 1.a $1$ $13.303$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots\)
1666.2.a.l 1666.a 1.a $1$ $13.303$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
1666.2.a.m 1666.a 1.a $1$ $13.303$ \(\Q\) None \(1\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots\)
1666.2.a.n 1666.a 1.a $1$ $13.303$ \(\Q\) None \(1\) \(2\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+4q^{5}+2q^{6}+q^{8}+\cdots\)
1666.2.a.o 1666.a 1.a $2$ $13.303$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
1666.2.a.p 1666.a 1.a $2$ $13.303$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(-2+\beta )q^{5}-\beta q^{6}+\cdots\)
1666.2.a.q 1666.a 1.a $2$ $13.303$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(2+\beta )q^{5}-\beta q^{6}+\cdots\)
1666.2.a.r 1666.a 1.a $2$ $13.303$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
1666.2.a.s 1666.a 1.a $2$ $13.303$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1-\beta )q^{5}+\cdots\)
1666.2.a.t 1666.a 1.a $3$ $13.303$ 3.3.404.1 None \(-3\) \(0\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{2}q^{5}+\cdots\)
1666.2.a.u 1666.a 1.a $3$ $13.303$ 3.3.404.1 None \(-3\) \(0\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots\)
1666.2.a.v 1666.a 1.a $4$ $13.303$ 4.4.4352.1 None \(-4\) \(0\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1666.2.a.w 1666.a 1.a $4$ $13.303$ 4.4.4352.1 None \(-4\) \(0\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
1666.2.a.x 1666.a 1.a $4$ $13.303$ 4.4.4352.1 None \(4\) \(-4\) \(-8\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
1666.2.a.y 1666.a 1.a $4$ $13.303$ 4.4.4352.1 None \(4\) \(4\) \(8\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
1666.2.a.z 1666.a 1.a $5$ $13.303$ 5.5.23949216.1 None \(5\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
1666.2.a.ba 1666.a 1.a $5$ $13.303$ 5.5.23949216.1 None \(5\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)

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

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