Properties

Label 2166.2.a
Level $2166$
Weight $2$
Character orbit 2166.a
Rep. character $\chi_{2166}(1,\cdot)$
Character field $\Q$
Dimension $57$
Newform subspaces $25$
Sturm bound $760$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2166.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(760\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2166))\).

Total New Old
Modular forms 420 57 363
Cusp forms 341 57 284
Eisenstein series 79 0 79

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

\(2\)\(3\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(11\)
Plus space\(+\)\(19\)
Minus space\(-\)\(38\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2166))\) 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 3 19
2166.2.a.a 2166.a 1.a $1$ $17.296$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
2166.2.a.b 2166.a 1.a $1$ $17.296$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
2166.2.a.c 2166.a 1.a $1$ $17.296$ \(\Q\) None \(-1\) \(1\) \(-4\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-4q^{5}-q^{6}-3q^{7}+\cdots\)
2166.2.a.d 2166.a 1.a $1$ $17.296$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
2166.2.a.e 2166.a 1.a $1$ $17.296$ \(\Q\) None \(-1\) \(1\) \(2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
2166.2.a.f 2166.a 1.a $1$ $17.296$ \(\Q\) None \(1\) \(-1\) \(-4\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-3q^{7}+\cdots\)
2166.2.a.g 2166.a 1.a $1$ $17.296$ \(\Q\) None \(1\) \(-1\) \(2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
2166.2.a.h 2166.a 1.a $1$ $17.296$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
2166.2.a.i 2166.a 1.a $1$ $17.296$ \(\Q\) None \(1\) \(1\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
2166.2.a.j 2166.a 1.a $2$ $17.296$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(5\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(3-\beta )q^{5}+q^{6}+\cdots\)
2166.2.a.k 2166.a 1.a $2$ $17.296$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots\)
2166.2.a.l 2166.a 1.a $2$ $17.296$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{8}+\cdots\)
2166.2.a.m 2166.a 1.a $2$ $17.296$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(5\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(3-\beta )q^{5}+q^{6}+\cdots\)
2166.2.a.n 2166.a 1.a $3$ $17.296$ \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(-6\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-2-\beta _{1})q^{5}+q^{6}+\cdots\)
2166.2.a.o 2166.a 1.a $3$ $17.296$ \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(0\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
2166.2.a.p 2166.a 1.a $3$ $17.296$ \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(-6\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-2+\beta _{1})q^{5}-q^{6}+\cdots\)
2166.2.a.q 2166.a 1.a $3$ $17.296$ \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(0\) \(-9\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
2166.2.a.r 2166.a 1.a $3$ $17.296$ \(\Q(\zeta_{18})^+\) None \(3\) \(-3\) \(-6\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}-q^{6}+\cdots\)
2166.2.a.s 2166.a 1.a $3$ $17.296$ \(\Q(\zeta_{18})^+\) None \(3\) \(-3\) \(0\) \(-9\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
2166.2.a.t 2166.a 1.a $3$ $17.296$ \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(-6\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2-\beta _{1})q^{5}+q^{6}+\cdots\)
2166.2.a.u 2166.a 1.a $3$ $17.296$ \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(0\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
2166.2.a.v 2166.a 1.a $4$ $17.296$ 4.4.40025.1 None \(-4\) \(-4\) \(2\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
2166.2.a.w 2166.a 1.a $4$ $17.296$ \(\Q(\zeta_{20})^+\) None \(-4\) \(4\) \(8\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(2+\beta _{1})q^{5}-q^{6}+\cdots\)
2166.2.a.x 2166.a 1.a $4$ $17.296$ \(\Q(\zeta_{20})^+\) None \(4\) \(-4\) \(8\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(2+\beta _{1})q^{5}-q^{6}+\cdots\)
2166.2.a.y 2166.a 1.a $4$ $17.296$ 4.4.40025.1 None \(4\) \(4\) \(2\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2166))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2166)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 2}\)