Properties

Label 6171.2.a
Level 6171
Weight 2
Character orbit a
Rep. character \(\chi_{6171}(1,\cdot)\)
Character field \(\Q\)
Dimension 290
Newform subspaces 45
Sturm bound 1584
Trace bound 7

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 6171 = 3 \cdot 11^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6171.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 45 \)
Sturm bound: \(1584\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6171))\).

Total New Old
Modular forms 816 290 526
Cusp forms 769 290 479
Eisenstein series 47 0 47

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

\(3\)\(11\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(34\)
\(+\)\(+\)\(-\)\(-\)\(42\)
\(+\)\(-\)\(+\)\(-\)\(40\)
\(+\)\(-\)\(-\)\(+\)\(30\)
\(-\)\(+\)\(+\)\(-\)\(38\)
\(-\)\(+\)\(-\)\(+\)\(30\)
\(-\)\(-\)\(+\)\(+\)\(33\)
\(-\)\(-\)\(-\)\(-\)\(43\)
Plus space\(+\)\(127\)
Minus space\(-\)\(163\)

Trace form

\( 290q + 4q^{2} - 2q^{3} + 292q^{4} + 2q^{6} + 4q^{7} + 290q^{9} + O(q^{10}) \) \( 290q + 4q^{2} - 2q^{3} + 292q^{4} + 2q^{6} + 4q^{7} + 290q^{9} + 4q^{10} + 2q^{12} - 6q^{13} + 6q^{15} + 304q^{16} + 4q^{18} + 2q^{19} + 8q^{20} - 12q^{21} + 8q^{23} + 6q^{24} + 292q^{25} + 36q^{26} - 2q^{27} + 8q^{29} + 8q^{30} - 8q^{31} + 24q^{32} - 4q^{34} - 20q^{35} + 292q^{36} + 12q^{37} - 20q^{38} - 4q^{39} + 24q^{40} + 24q^{41} - 16q^{42} - 2q^{43} + 20q^{46} + 12q^{47} + 2q^{48} + 306q^{49} + 8q^{50} + 4q^{51} - 60q^{52} + 12q^{53} + 2q^{54} - 16q^{57} + 48q^{58} + 24q^{60} - 4q^{61} + 8q^{62} + 4q^{63} + 368q^{64} + 56q^{65} - 24q^{67} - 2q^{69} - 8q^{70} + 32q^{71} + 24q^{73} + 16q^{74} + 2q^{75} + 12q^{76} + 40q^{78} - 20q^{79} - 64q^{80} + 290q^{81} + 20q^{82} + 28q^{83} - 24q^{84} + 6q^{85} + 44q^{86} + 68q^{89} + 4q^{90} - 84q^{91} - 8q^{92} - 68q^{93} - 48q^{94} - 8q^{95} + 14q^{96} - 32q^{97} - 12q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6171))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 11 17
6171.2.a.a \(1\) \(49.276\) \(\Q\) None \(-2\) \(1\) \(2\) \(-3\) \(-\) \(-\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+2q^{5}-2q^{6}+\cdots\)
6171.2.a.b \(1\) \(49.276\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}-q^{6}+2q^{7}+3q^{8}+\cdots\)
6171.2.a.c \(1\) \(49.276\) \(\Q\) None \(0\) \(-1\) \(-2\) \(3\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{4}-2q^{5}+3q^{7}+q^{9}+2q^{12}+\cdots\)
6171.2.a.d \(1\) \(49.276\) \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}-2q^{5}-q^{7}+q^{9}-2q^{12}+\cdots\)
6171.2.a.e \(1\) \(49.276\) \(\Q\) None \(0\) \(1\) \(3\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}+3q^{5}+4q^{7}+q^{9}-2q^{12}+\cdots\)
6171.2.a.f \(1\) \(49.276\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots\)
6171.2.a.g \(1\) \(49.276\) \(\Q\) None \(1\) \(1\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-3q^{8}+\cdots\)
6171.2.a.h \(1\) \(49.276\) \(\Q\) None \(2\) \(1\) \(0\) \(3\) \(-\) \(-\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots\)
6171.2.a.i \(1\) \(49.276\) \(\Q\) None \(2\) \(1\) \(2\) \(3\) \(-\) \(-\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{5}+2q^{6}+\cdots\)
6171.2.a.j \(2\) \(49.276\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(-6\) \(-4\) \(+\) \(+\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}-3q^{5}+\cdots\)
6171.2.a.k \(2\) \(49.276\) \(\Q(\sqrt{17}) \) None \(-1\) \(-2\) \(4\) \(-1\) \(+\) \(-\) \(-\) \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+2q^{5}+\beta q^{6}+\cdots\)
6171.2.a.l \(2\) \(49.276\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(q+(1-2\beta )q^{2}-q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots\)
6171.2.a.m \(2\) \(49.276\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(1\) \(4\) \(+\) \(+\) \(+\) \(q+(1-2\beta )q^{2}-q^{3}+3q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
6171.2.a.n \(2\) \(49.276\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-4\) \(6\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+q^{3}+(-2+\beta )q^{5}+\beta q^{6}+\cdots\)
6171.2.a.o \(2\) \(49.276\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(-6\) \(4\) \(+\) \(-\) \(-\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-3q^{5}+\cdots\)
6171.2.a.p \(2\) \(49.276\) \(\Q(\sqrt{17}) \) None \(1\) \(-2\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q+\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
6171.2.a.q \(3\) \(49.276\) 3.3.316.1 None \(-1\) \(-3\) \(4\) \(-2\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
6171.2.a.r \(3\) \(49.276\) 3.3.148.1 None \(0\) \(-3\) \(-4\) \(7\) \(+\) \(-\) \(+\) \(q+\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
6171.2.a.s \(3\) \(49.276\) 3.3.148.1 None \(2\) \(-3\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
6171.2.a.t \(4\) \(49.276\) 4.4.22676.1 None \(-1\) \(4\) \(-4\) \(-9\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
6171.2.a.u \(5\) \(49.276\) 5.5.749264.1 None \(-2\) \(5\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
6171.2.a.v \(5\) \(49.276\) 5.5.749264.1 None \(2\) \(5\) \(0\) \(3\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
6171.2.a.w \(6\) \(49.276\) 6.6.46051664.1 None \(-1\) \(-6\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
6171.2.a.x \(6\) \(49.276\) 6.6.29995216.1 None \(-1\) \(-6\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{3}-\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots\)
6171.2.a.y \(6\) \(49.276\) 6.6.4642000.1 None \(-1\) \(6\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
6171.2.a.z \(6\) \(49.276\) 6.6.29995216.1 None \(1\) \(-6\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{3}-\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots\)
6171.2.a.ba \(6\) \(49.276\) 6.6.46051664.1 None \(1\) \(-6\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
6171.2.a.bb \(6\) \(49.276\) 6.6.4642000.1 None \(1\) \(6\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
6171.2.a.bc \(6\) \(49.276\) 6.6.78067472.1 None \(1\) \(6\) \(2\) \(-7\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
6171.2.a.bd \(7\) \(49.276\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(7\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
6171.2.a.be \(7\) \(49.276\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(7\) \(0\) \(3\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
6171.2.a.bf \(8\) \(49.276\) 8.8.\(\cdots\).1 None \(-4\) \(-8\) \(-5\) \(1\) \(+\) \(-\) \(-\) \(q-\beta _{3}q^{2}-q^{3}+(-1+\beta _{3}-\beta _{5})q^{4}+\cdots\)
6171.2.a.bg \(8\) \(49.276\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(-8\) \(0\) \(3\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
6171.2.a.bh \(8\) \(49.276\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-8\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
6171.2.a.bi \(8\) \(49.276\) 8.8.\(\cdots\).1 None \(4\) \(-8\) \(-5\) \(-1\) \(+\) \(+\) \(+\) \(q+\beta _{3}q^{2}-q^{3}+(-1+\beta _{3}-\beta _{5})q^{4}+\cdots\)
6171.2.a.bj \(12\) \(49.276\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(12\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
6171.2.a.bk \(12\) \(49.276\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(12\) \(-14\) \(-5\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{3}+\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots\)
6171.2.a.bl \(12\) \(49.276\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(12\) \(-14\) \(5\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{3}+\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots\)
6171.2.a.bm \(12\) \(49.276\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(12\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
6171.2.a.bn \(14\) \(49.276\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-14\) \(0\) \(6\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
6171.2.a.bo \(14\) \(49.276\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(-14\) \(0\) \(-6\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
6171.2.a.bp \(20\) \(49.276\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-3\) \(-20\) \(7\) \(5\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots\)
6171.2.a.bq \(20\) \(49.276\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-1\) \(20\) \(17\) \(-1\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{13}+\cdots)q^{5}+\cdots\)
6171.2.a.br \(20\) \(49.276\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(1\) \(20\) \(17\) \(1\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{13}+\cdots)q^{5}+\cdots\)
6171.2.a.bs \(20\) \(49.276\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(3\) \(-20\) \(7\) \(-5\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6171))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6171)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2057))\)\(^{\oplus 2}\)