Properties

Label 5586.2.a
Level $5586$
Weight $2$
Character orbit 5586.a
Rep. character $\chi_{5586}(1,\cdot)$
Character field $\Q$
Dimension $124$
Newform subspaces $58$
Sturm bound $2240$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5586.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 58 \)
Sturm bound: \(2240\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5586))\).

Total New Old
Modular forms 1152 124 1028
Cusp forms 1089 124 965
Eisenstein series 63 0 63

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

\(2\)\(3\)\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(10\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(10\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(12\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(48\)
Minus space\(-\)\(76\)

Trace form

\( 124q + 2q^{2} + 124q^{4} - 2q^{6} + 2q^{8} + 124q^{9} + O(q^{10}) \) \( 124q + 2q^{2} + 124q^{4} - 2q^{6} + 2q^{8} + 124q^{9} + 4q^{11} + 12q^{13} - 4q^{15} + 124q^{16} + 8q^{17} + 2q^{18} - 2q^{19} - 4q^{22} + 4q^{23} - 2q^{24} + 124q^{25} + 12q^{26} - 4q^{29} + 4q^{30} + 4q^{31} + 2q^{32} + 4q^{33} + 20q^{34} + 124q^{36} - 12q^{37} + 8q^{39} - 12q^{41} + 8q^{43} + 4q^{44} - 28q^{47} + 78q^{50} - 16q^{51} + 12q^{52} + 68q^{53} - 2q^{54} - 48q^{55} + 2q^{57} + 64q^{58} - 4q^{60} + 16q^{61} - 16q^{62} + 124q^{64} + 40q^{65} + 4q^{66} - 16q^{67} + 8q^{68} - 8q^{69} - 16q^{71} + 2q^{72} + 68q^{74} - 2q^{76} - 8q^{78} + 36q^{79} + 124q^{81} - 32q^{82} - 20q^{83} + 48q^{85} - 24q^{86} - 12q^{87} - 4q^{88} + 12q^{89} + 4q^{92} + 24q^{93} + 40q^{94} - 4q^{95} - 2q^{96} - 16q^{97} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5586))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 19
5586.2.a.a \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.b \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.c \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.d \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.e \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.f \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.g \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.h \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.i \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.j \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.k \(1\) \(44.604\) \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.l \(1\) \(44.604\) \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.m \(1\) \(44.604\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.n \(1\) \(44.604\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.o \(1\) \(44.604\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.p \(1\) \(44.604\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5586.2.a.q \(1\) \(44.604\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.r \(1\) \(44.604\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.s \(1\) \(44.604\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.t \(1\) \(44.604\) \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.u \(1\) \(44.604\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
5586.2.a.v \(1\) \(44.604\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.w \(1\) \(44.604\) \(\Q\) None \(1\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.x \(1\) \(44.604\) \(\Q\) None \(1\) \(-1\) \(4\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.y \(1\) \(44.604\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.z \(1\) \(44.604\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.ba \(1\) \(44.604\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.bb \(1\) \(44.604\) \(\Q\) None \(1\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.bc \(2\) \(44.604\) \(\Q(\sqrt{7}) \) None \(-2\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bd \(2\) \(44.604\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.be \(2\) \(44.604\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bf \(2\) \(44.604\) \(\Q(\sqrt{7}) \) None \(-2\) \(2\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bg \(2\) \(44.604\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-6\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-3+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bh \(2\) \(44.604\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bi \(2\) \(44.604\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bj \(2\) \(44.604\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
5586.2.a.bk \(2\) \(44.604\) \(\Q(\sqrt{7}) \) None \(2\) \(-2\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bl \(2\) \(44.604\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(4\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots\)
5586.2.a.bm \(2\) \(44.604\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bn \(2\) \(44.604\) \(\Q(\sqrt{7}) \) None \(2\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bo \(2\) \(44.604\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
5586.2.a.bp \(2\) \(44.604\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.bq \(2\) \(44.604\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.br \(2\) \(44.604\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(6\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(3+\beta )q^{5}+q^{6}+\cdots\)
5586.2.a.bs \(3\) \(44.604\) 3.3.404.1 None \(-3\) \(-3\) \(1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.bt \(3\) \(44.604\) 3.3.404.1 None \(-3\) \(3\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.bu \(3\) \(44.604\) 3.3.404.1 None \(3\) \(-3\) \(5\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(2-\beta _{1})q^{5}-q^{6}+\cdots\)
5586.2.a.bv \(3\) \(44.604\) 3.3.404.1 None \(3\) \(3\) \(-5\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-2+\beta _{1})q^{5}+q^{6}+\cdots\)
5586.2.a.bw \(4\) \(44.604\) 4.4.29268.1 None \(-4\) \(-4\) \(0\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.bx \(4\) \(44.604\) 4.4.4352.1 None \(-4\) \(-4\) \(4\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{3})q^{5}+q^{6}+\cdots\)
5586.2.a.by \(4\) \(44.604\) 4.4.4352.1 None \(-4\) \(4\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(-1-\beta _{3})q^{5}-q^{6}+\cdots\)
5586.2.a.bz \(4\) \(44.604\) 4.4.29268.1 None \(-4\) \(4\) \(0\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.ca \(4\) \(44.604\) 4.4.202932.1 None \(4\) \(-4\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.cb \(4\) \(44.604\) 4.4.202932.1 None \(4\) \(4\) \(2\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+q^{8}+\cdots\)
5586.2.a.cc \(6\) \(44.604\) 6.6.207085568.1 None \(-6\) \(-6\) \(0\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta _{5}q^{5}+q^{6}-q^{8}+\cdots\)
5586.2.a.cd \(6\) \(44.604\) 6.6.207085568.1 None \(-6\) \(6\) \(0\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-\beta _{5}q^{5}-q^{6}-q^{8}+\cdots\)
5586.2.a.ce \(8\) \(44.604\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-8\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-\beta _{7}q^{5}-q^{6}+q^{8}+\cdots\)
5586.2.a.cf \(8\) \(44.604\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(8\) \(4\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+\beta _{7}q^{5}+q^{6}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5586))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5586)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(798))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1862))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2793))\)\(^{\oplus 2}\)