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Properties

Label 2166.4.a
Level $2166$
Weight $4$
Character orbit 2166.a
Rep. character $\chi_{2166}(1,\cdot)$
Character field $\Q$
Dimension $171$
Newform subspaces $41$
Sturm bound $1520$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2166.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 41 \)
Sturm bound: \(1520\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2166))\).

Total New Old
Modular forms 1180 171 1009
Cusp forms 1100 171 929
Eisenstein series 80 0 80

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
\(+\)\(+\)\(+\)$+$\(24\)
\(+\)\(+\)\(-\)$-$\(19\)
\(+\)\(-\)\(+\)$-$\(21\)
\(+\)\(-\)\(-\)$+$\(22\)
\(-\)\(+\)\(+\)$-$\(19\)
\(-\)\(+\)\(-\)$+$\(23\)
\(-\)\(-\)\(+\)$+$\(26\)
\(-\)\(-\)\(-\)$-$\(17\)
Plus space\(+\)\(95\)
Minus space\(-\)\(76\)

Trace form

\( 171 q - 2 q^{2} + 3 q^{3} + 684 q^{4} - 26 q^{5} + 6 q^{6} + 28 q^{7} - 8 q^{8} + 1539 q^{9} + O(q^{10}) \) \( 171 q - 2 q^{2} + 3 q^{3} + 684 q^{4} - 26 q^{5} + 6 q^{6} + 28 q^{7} - 8 q^{8} + 1539 q^{9} - 52 q^{10} + 68 q^{11} + 12 q^{12} - 58 q^{13} - 32 q^{14} - 66 q^{15} + 2736 q^{16} - 6 q^{17} - 18 q^{18} - 104 q^{20} - 48 q^{21} - 144 q^{22} - 376 q^{23} + 24 q^{24} + 4473 q^{25} + 148 q^{26} + 27 q^{27} + 112 q^{28} + 406 q^{29} + 84 q^{30} + 220 q^{31} - 32 q^{32} + 216 q^{33} - 260 q^{34} + 1072 q^{35} + 6156 q^{36} + 366 q^{37} + 138 q^{39} - 208 q^{40} - 454 q^{41} - 144 q^{42} + 760 q^{43} + 272 q^{44} - 234 q^{45} + 432 q^{46} + 1208 q^{47} + 48 q^{48} + 9599 q^{49} - 142 q^{50} + 174 q^{51} - 232 q^{52} - 266 q^{53} + 54 q^{54} - 936 q^{55} - 128 q^{56} + 532 q^{58} + 1156 q^{59} - 264 q^{60} + 746 q^{61} + 1584 q^{62} + 252 q^{63} + 10944 q^{64} - 260 q^{65} - 168 q^{66} - 852 q^{67} - 24 q^{68} + 792 q^{69} + 768 q^{70} - 728 q^{71} - 72 q^{72} + 1886 q^{73} + 20 q^{74} + 1413 q^{75} - 184 q^{77} - 756 q^{78} - 620 q^{79} - 416 q^{80} + 13851 q^{81} + 1436 q^{82} + 100 q^{83} - 192 q^{84} + 164 q^{85} + 1992 q^{86} - 42 q^{87} - 576 q^{88} - 2726 q^{89} - 468 q^{90} - 2136 q^{91} - 1504 q^{92} + 300 q^{93} - 240 q^{94} + 96 q^{96} - 946 q^{97} - 1426 q^{98} + 612 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2166))\) 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
2166.4.a.a 2166.a 1.a $1$ $127.798$ \(\Q\) None \(-2\) \(3\) \(-11\) \(-15\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-11q^{5}-6q^{6}+\cdots\)
2166.4.a.b 2166.a 1.a $1$ $127.798$ \(\Q\) None \(-2\) \(3\) \(-6\) \(19\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots\)
2166.4.a.c 2166.a 1.a $1$ $127.798$ \(\Q\) None \(-2\) \(3\) \(2\) \(-21\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
2166.4.a.d 2166.a 1.a $1$ $127.798$ \(\Q\) None \(2\) \(-3\) \(-7\) \(-15\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-7q^{5}-6q^{6}+\cdots\)
2166.4.a.e 2166.a 1.a $1$ $127.798$ \(\Q\) None \(2\) \(-3\) \(-6\) \(19\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots\)
2166.4.a.f 2166.a 1.a $1$ $127.798$ \(\Q\) None \(2\) \(-3\) \(2\) \(-21\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
2166.4.a.g 2166.a 1.a $1$ $127.798$ \(\Q\) None \(2\) \(-3\) \(12\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+12q^{5}-6q^{6}+\cdots\)
2166.4.a.h 2166.a 1.a $1$ $127.798$ \(\Q\) None \(2\) \(3\) \(-19\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-19q^{5}+6q^{6}+\cdots\)
2166.4.a.i 2166.a 1.a $1$ $127.798$ \(\Q\) None \(2\) \(3\) \(6\) \(-16\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
2166.4.a.j 2166.a 1.a $2$ $127.798$ \(\Q(\sqrt{5}) \) None \(-4\) \(-6\) \(-13\) \(-17\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(-4-5\beta )q^{5}+\cdots\)
2166.4.a.k 2166.a 1.a $2$ $127.798$ \(\Q(\sqrt{30}) \) None \(-4\) \(-6\) \(8\) \(18\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(4+\beta )q^{5}+6q^{6}+\cdots\)
2166.4.a.l 2166.a 1.a $2$ $127.798$ \(\Q(\sqrt{273}) \) None \(-4\) \(-6\) \(11\) \(9\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(6-\beta )q^{5}+6q^{6}+\cdots\)
2166.4.a.m 2166.a 1.a $2$ $127.798$ \(\Q(\sqrt{313}) \) None \(-4\) \(6\) \(-15\) \(9\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(-7-\beta )q^{5}+\cdots\)
2166.4.a.n 2166.a 1.a $2$ $127.798$ \(\Q(\sqrt{17}) \) None \(-4\) \(6\) \(18\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(9+\beta )q^{5}-6q^{6}+\cdots\)
2166.4.a.o 2166.a 1.a $2$ $127.798$ \(\Q(\sqrt{313}) \) None \(4\) \(-6\) \(-15\) \(9\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-7-\beta )q^{5}+\cdots\)
2166.4.a.p 2166.a 1.a $2$ $127.798$ \(\Q(\sqrt{5}) \) None \(4\) \(6\) \(-13\) \(-17\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-4-5\beta )q^{5}+\cdots\)
2166.4.a.q 2166.a 1.a $2$ $127.798$ \(\Q(\sqrt{30}) \) None \(4\) \(6\) \(8\) \(18\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(4+\beta )q^{5}+6q^{6}+\cdots\)
2166.4.a.r 2166.a 1.a $3$ $127.798$ 3.3.373564.1 None \(-6\) \(-9\) \(-5\) \(-11\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(-2+\beta _{2})q^{5}+\cdots\)
2166.4.a.s 2166.a 1.a $3$ $127.798$ 3.3.1524.1 None \(-6\) \(-9\) \(2\) \(-17\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(1-\beta _{2})q^{5}+\cdots\)
2166.4.a.t 2166.a 1.a $3$ $127.798$ 3.3.14457.1 None \(-6\) \(9\) \(10\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(3-\beta _{1})q^{5}+\cdots\)
2166.4.a.u 2166.a 1.a $3$ $127.798$ 3.3.14457.1 None \(6\) \(-9\) \(10\) \(7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(3-\beta _{1})q^{5}+\cdots\)
2166.4.a.v 2166.a 1.a $3$ $127.798$ 3.3.373564.1 None \(6\) \(9\) \(-5\) \(-11\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-2+\beta _{2})q^{5}+\cdots\)
2166.4.a.w 2166.a 1.a $3$ $127.798$ 3.3.1524.1 None \(6\) \(9\) \(2\) \(-17\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(1-\beta _{2})q^{5}+\cdots\)
2166.4.a.x 2166.a 1.a $4$ $127.798$ 4.4.184225.1 None \(-8\) \(-12\) \(-28\) \(-17\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(-7+2\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.y 2166.a 1.a $4$ $127.798$ 4.4.8742025.2 None \(-8\) \(12\) \(0\) \(28\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
2166.4.a.z 2166.a 1.a $4$ $127.798$ 4.4.8742025.2 None \(8\) \(-12\) \(0\) \(28\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
2166.4.a.ba 2166.a 1.a $4$ $127.798$ 4.4.184225.1 None \(8\) \(12\) \(-28\) \(-17\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-7+2\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.bb 2166.a 1.a $6$ $127.798$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(-18\) \(-3\) \(-12\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
2166.4.a.bc 2166.a 1.a $6$ $127.798$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(18\) \(-1\) \(28\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(1-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.bd 2166.a 1.a $6$ $127.798$ 6.6.\(\cdots\).1 None \(-12\) \(18\) \(27\) \(-42\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(4+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.be 2166.a 1.a $6$ $127.798$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(-18\) \(-1\) \(28\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(1-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.bf 2166.a 1.a $6$ $127.798$ 6.6.\(\cdots\).1 None \(12\) \(-18\) \(27\) \(-42\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(4+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.bg 2166.a 1.a $6$ $127.798$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(18\) \(-3\) \(-12\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
2166.4.a.bh 2166.a 1.a $8$ $127.798$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(24\) \(-30\) \(-34\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(-4-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
2166.4.a.bi 2166.a 1.a $8$ $127.798$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(16\) \(-24\) \(-30\) \(-34\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-4-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
2166.4.a.bj 2166.a 1.a $9$ $127.798$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-18\) \(-27\) \(27\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots\)
2166.4.a.bk 2166.a 1.a $9$ $127.798$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-18\) \(27\) \(-3\) \(30\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+\beta _{1}q^{5}-6q^{6}+\cdots\)
2166.4.a.bl 2166.a 1.a $9$ $127.798$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(18\) \(-27\) \(-3\) \(30\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+\beta _{1}q^{5}-6q^{6}+\cdots\)
2166.4.a.bm 2166.a 1.a $9$ $127.798$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(18\) \(27\) \(27\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots\)
2166.4.a.bn 2166.a 1.a $12$ $127.798$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-24\) \(-36\) \(10\) \(56\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(1+\beta _{2})q^{5}+\cdots\)
2166.4.a.bo 2166.a 1.a $12$ $127.798$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(24\) \(36\) \(10\) \(56\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(1+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2166))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2166)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 2}\)