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

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2166))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 19
2166.4.a.a \(1\) \(127.798\) \(\Q\) None \(-2\) \(3\) \(-11\) \(-15\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}-11q^{5}-6q^{6}+\cdots\)
2166.4.a.b \(1\) \(127.798\) \(\Q\) None \(-2\) \(3\) \(-6\) \(19\) \(+\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots\)
2166.4.a.c \(1\) \(127.798\) \(\Q\) None \(-2\) \(3\) \(2\) \(-21\) \(+\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
2166.4.a.d \(1\) \(127.798\) \(\Q\) None \(2\) \(-3\) \(-7\) \(-15\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-7q^{5}-6q^{6}+\cdots\)
2166.4.a.e \(1\) \(127.798\) \(\Q\) None \(2\) \(-3\) \(-6\) \(19\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots\)
2166.4.a.f \(1\) \(127.798\) \(\Q\) None \(2\) \(-3\) \(2\) \(-21\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
2166.4.a.g \(1\) \(127.798\) \(\Q\) None \(2\) \(-3\) \(12\) \(4\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+12q^{5}-6q^{6}+\cdots\)
2166.4.a.h \(1\) \(127.798\) \(\Q\) None \(2\) \(3\) \(-19\) \(9\) \(-\) \(-\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}-19q^{5}+6q^{6}+\cdots\)
2166.4.a.i \(1\) \(127.798\) \(\Q\) None \(2\) \(3\) \(6\) \(-16\) \(-\) \(-\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
2166.4.a.j \(2\) \(127.798\) \(\Q(\sqrt{5}) \) None \(-4\) \(-6\) \(-13\) \(-17\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+(-4-5\beta )q^{5}+\cdots\)
2166.4.a.k \(2\) \(127.798\) \(\Q(\sqrt{30}) \) None \(-4\) \(-6\) \(8\) \(18\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+(4+\beta )q^{5}+6q^{6}+\cdots\)
2166.4.a.l \(2\) \(127.798\) \(\Q(\sqrt{273}) \) None \(-4\) \(-6\) \(11\) \(9\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+(6-\beta )q^{5}+6q^{6}+\cdots\)
2166.4.a.m \(2\) \(127.798\) \(\Q(\sqrt{313}) \) None \(-4\) \(6\) \(-15\) \(9\) \(+\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+(-7-\beta )q^{5}+\cdots\)
2166.4.a.n \(2\) \(127.798\) \(\Q(\sqrt{17}) \) None \(-4\) \(6\) \(18\) \(4\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(9+\beta )q^{5}-6q^{6}+\cdots\)
2166.4.a.o \(2\) \(127.798\) \(\Q(\sqrt{313}) \) None \(4\) \(-6\) \(-15\) \(9\) \(-\) \(+\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}+(-7-\beta )q^{5}+\cdots\)
2166.4.a.p \(2\) \(127.798\) \(\Q(\sqrt{5}) \) None \(4\) \(6\) \(-13\) \(-17\) \(-\) \(-\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+(-4-5\beta )q^{5}+\cdots\)
2166.4.a.q \(2\) \(127.798\) \(\Q(\sqrt{30}) \) None \(4\) \(6\) \(8\) \(18\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+(4+\beta )q^{5}+6q^{6}+\cdots\)
2166.4.a.r \(3\) \(127.798\) 3.3.373564.1 None \(-6\) \(-9\) \(-5\) \(-11\) \(+\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+(-2+\beta _{2})q^{5}+\cdots\)
2166.4.a.s \(3\) \(127.798\) 3.3.1524.1 None \(-6\) \(-9\) \(2\) \(-17\) \(+\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+(1-\beta _{2})q^{5}+\cdots\)
2166.4.a.t \(3\) \(127.798\) 3.3.14457.1 None \(-6\) \(9\) \(10\) \(7\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(3-\beta _{1})q^{5}+\cdots\)
2166.4.a.u \(3\) \(127.798\) 3.3.14457.1 None \(6\) \(-9\) \(10\) \(7\) \(-\) \(+\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}+(3-\beta _{1})q^{5}+\cdots\)
2166.4.a.v \(3\) \(127.798\) 3.3.373564.1 None \(6\) \(9\) \(-5\) \(-11\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+(-2+\beta _{2})q^{5}+\cdots\)
2166.4.a.w \(3\) \(127.798\) 3.3.1524.1 None \(6\) \(9\) \(2\) \(-17\) \(-\) \(-\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+(1-\beta _{2})q^{5}+\cdots\)
2166.4.a.x \(4\) \(127.798\) 4.4.184225.1 None \(-8\) \(-12\) \(-28\) \(-17\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+(-7+2\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.y \(4\) \(127.798\) 4.4.8742025.2 None \(-8\) \(12\) \(0\) \(28\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
2166.4.a.z \(4\) \(127.798\) 4.4.8742025.2 None \(8\) \(-12\) \(0\) \(28\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
2166.4.a.ba \(4\) \(127.798\) 4.4.184225.1 None \(8\) \(12\) \(-28\) \(-17\) \(-\) \(-\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+(-7+2\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.bb \(6\) \(127.798\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(-18\) \(-3\) \(-12\) \(+\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
2166.4.a.bc \(6\) \(127.798\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(18\) \(-1\) \(28\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(1-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.bd \(6\) \(127.798\) 6.6.\(\cdots\).1 None \(-12\) \(18\) \(27\) \(-42\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(4+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.be \(6\) \(127.798\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(-18\) \(-1\) \(28\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+(1-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.bf \(6\) \(127.798\) 6.6.\(\cdots\).1 None \(12\) \(-18\) \(27\) \(-42\) \(-\) \(+\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}+(4+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
2166.4.a.bg \(6\) \(127.798\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(18\) \(-3\) \(-12\) \(-\) \(-\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
2166.4.a.bh \(8\) \(127.798\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(24\) \(-30\) \(-34\) \(+\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+(-4-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
2166.4.a.bi \(8\) \(127.798\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(16\) \(-24\) \(-30\) \(-34\) \(-\) \(+\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}+(-4-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
2166.4.a.bj \(9\) \(127.798\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-18\) \(-27\) \(27\) \(0\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots\)
2166.4.a.bk \(9\) \(127.798\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-18\) \(27\) \(-3\) \(30\) \(+\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+\beta _{1}q^{5}-6q^{6}+\cdots\)
2166.4.a.bl \(9\) \(127.798\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(18\) \(-27\) \(-3\) \(30\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+\beta _{1}q^{5}-6q^{6}+\cdots\)
2166.4.a.bm \(9\) \(127.798\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(18\) \(27\) \(27\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots\)
2166.4.a.bn \(12\) \(127.798\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-24\) \(-36\) \(10\) \(56\) \(+\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+(1+\beta _{2})q^{5}+\cdots\)
2166.4.a.bo \(12\) \(127.798\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(24\) \(36\) \(10\) \(56\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+(1+\beta _{2})q^{5}+\cdots\)

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

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