Properties

Label 6027.2.a
Level 6027
Weight 2
Character orbit a
Rep. character \(\chi_{6027}(1,\cdot)\)
Character field \(\Q\)
Dimension 274
Newforms 41
Sturm bound 1568
Trace bound 5

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Defining parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)
Character field: \(\Q\)
Newforms: \( 41 \)
Sturm bound: \(1568\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6027))\).

Total New Old
Modular forms 800 274 526
Cusp forms 769 274 495
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.

\(3\)\(7\)\(41\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(30\)
\(+\)\(+\)\(-\)\(-\)\(38\)
\(+\)\(-\)\(+\)\(-\)\(37\)
\(+\)\(-\)\(-\)\(+\)\(31\)
\(-\)\(+\)\(+\)\(-\)\(37\)
\(-\)\(+\)\(-\)\(+\)\(29\)
\(-\)\(-\)\(+\)\(+\)\(33\)
\(-\)\(-\)\(-\)\(-\)\(39\)
Plus space\(+\)\(123\)
Minus space\(-\)\(151\)

Trace form

\( 274q + 4q^{2} + 2q^{3} + 276q^{4} + 4q^{5} - 2q^{6} + 12q^{8} + 274q^{9} + O(q^{10}) \) \( 274q + 4q^{2} + 2q^{3} + 276q^{4} + 4q^{5} - 2q^{6} + 12q^{8} + 274q^{9} + 12q^{11} + 6q^{12} + 12q^{13} + 296q^{16} + 8q^{17} + 4q^{18} + 4q^{19} + 12q^{20} - 4q^{22} + 12q^{23} - 6q^{24} + 294q^{25} - 12q^{26} + 2q^{27} + 20q^{29} + 12q^{30} - 14q^{31} + 8q^{32} + 10q^{33} + 24q^{34} + 276q^{36} - 6q^{37} - 12q^{38} - 24q^{39} - 32q^{40} + 6q^{43} + 52q^{44} + 4q^{45} - 8q^{47} + 14q^{48} + 32q^{50} - 10q^{51} + 52q^{52} + 28q^{53} - 2q^{54} + 16q^{55} - 16q^{57} - 4q^{58} + 16q^{59} + 24q^{60} + 6q^{61} + 16q^{62} + 368q^{64} - 4q^{65} - 24q^{66} - 20q^{67} - 4q^{68} - 8q^{69} + 40q^{71} + 12q^{72} + 30q^{73} + 40q^{74} + 6q^{75} - 28q^{76} + 40q^{78} - 20q^{79} + 40q^{80} + 274q^{81} + 4q^{82} - 48q^{83} + 44q^{85} - 92q^{86} + 14q^{87} - 124q^{88} - 48q^{89} - 100q^{92} - 12q^{93} - 56q^{94} + 20q^{95} - 34q^{96} + 32q^{97} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6027))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 41
6027.2.a.a \(1\) \(48.126\) \(\Q\) None \(-2\) \(-1\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
6027.2.a.b \(1\) \(48.126\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}+3q^{8}+\cdots\)
6027.2.a.c \(1\) \(48.126\) \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}-q^{4}+3q^{5}+q^{6}+3q^{8}+\cdots\)
6027.2.a.d \(1\) \(48.126\) \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}+3q^{8}+\cdots\)
6027.2.a.e \(1\) \(48.126\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}+2q^{5}+q^{9}+5q^{11}+\cdots\)
6027.2.a.f \(1\) \(48.126\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots\)
6027.2.a.g \(1\) \(48.126\) \(\Q\) None \(2\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{9}+4q^{11}+\cdots\)
6027.2.a.h \(1\) \(48.126\) \(\Q\) None \(2\) \(1\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{9}+4q^{11}+\cdots\)
6027.2.a.i \(2\) \(48.126\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+q^{5}+\cdots\)
6027.2.a.j \(2\) \(48.126\) \(\Q(\sqrt{17}) \) None \(-1\) \(-2\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(2-\beta )q^{5}+\cdots\)
6027.2.a.k \(2\) \(48.126\) \(\Q(\sqrt{17}) \) None \(-1\) \(2\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-2q^{5}-\beta q^{6}+\cdots\)
6027.2.a.l \(2\) \(48.126\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{4}-2\beta q^{5}+q^{9}+(4+\beta )q^{11}+\cdots\)
6027.2.a.m \(2\) \(48.126\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(q+\beta q^{2}-q^{3}+(-2+\beta )q^{5}-\beta q^{6}+\cdots\)
6027.2.a.n \(2\) \(48.126\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}-2\beta q^{5}+q^{9}+(4-\beta )q^{11}+\cdots\)
6027.2.a.o \(3\) \(48.126\) 3.3.148.1 None \(-1\) \(3\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
6027.2.a.p \(3\) \(48.126\) 3.3.1620.1 None \(0\) \(-3\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{4}-\beta _{1}q^{5}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
6027.2.a.q \(3\) \(48.126\) 3.3.1620.1 None \(0\) \(3\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}+\beta _{1}q^{5}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
6027.2.a.r \(3\) \(48.126\) 3.3.785.1 None \(1\) \(-3\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
6027.2.a.s \(3\) \(48.126\) 3.3.316.1 None \(1\) \(3\) \(-4\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
6027.2.a.t \(3\) \(48.126\) 3.3.785.1 None \(1\) \(3\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
6027.2.a.u \(4\) \(48.126\) 4.4.8468.1 None \(1\) \(4\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
6027.2.a.v \(5\) \(48.126\) 5.5.981328.1 None \(-3\) \(5\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
6027.2.a.w \(5\) \(48.126\) 5.5.626512.1 None \(3\) \(-5\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
6027.2.a.x \(5\) \(48.126\) 5.5.1197392.1 None \(3\) \(5\) \(9\) \(0\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
6027.2.a.y \(7\) \(48.126\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(-7\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
6027.2.a.z \(8\) \(48.126\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(-8\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
6027.2.a.ba \(8\) \(48.126\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(8\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
6027.2.a.bb \(8\) \(48.126\) 8.8.7457527933.1 None \(1\) \(-8\) \(-7\) \(0\) \(+\) \(+\) \(+\) \(q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(2+\beta _{6})q^{4}+\cdots\)
6027.2.a.bc \(8\) \(48.126\) 8.8.7457527933.1 None \(1\) \(8\) \(7\) \(0\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1}-\beta _{2})q^{2}+q^{3}+(2+\beta _{6})q^{4}+\cdots\)
6027.2.a.bd \(10\) \(48.126\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(-10\) \(-6\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots\)
6027.2.a.be \(10\) \(48.126\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(10\) \(6\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots\)
6027.2.a.bf \(12\) \(48.126\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(-12\) \(-12\) \(0\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots\)
6027.2.a.bg \(12\) \(48.126\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(12\) \(12\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots\)
6027.2.a.bh \(13\) \(48.126\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-4\) \(-13\) \(8\) \(0\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{8}+\cdots)q^{5}+\cdots\)
6027.2.a.bi \(13\) \(48.126\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-4\) \(13\) \(-8\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{8}+\cdots)q^{5}+\cdots\)
6027.2.a.bj \(14\) \(48.126\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-14\) \(10\) \(0\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
6027.2.a.bk \(14\) \(48.126\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(14\) \(-10\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{3}+\cdots)q^{5}+\cdots\)
6027.2.a.bl \(16\) \(48.126\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(-16\) \(12\) \(0\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{5}+\cdots)q^{5}+\cdots\)
6027.2.a.bm \(16\) \(48.126\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(16\) \(-12\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
6027.2.a.bn \(24\) \(48.126\) None \(8\) \(-24\) \(-4\) \(0\) \(+\) \(+\) \(-\)
6027.2.a.bo \(24\) \(48.126\) None \(8\) \(24\) \(4\) \(0\) \(-\) \(+\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6027))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6027)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(861))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2009))\)\(^{\oplus 2}\)