Properties

Label 5577.2.a
Level $5577$
Weight $2$
Character orbit 5577.a
Rep. character $\chi_{5577}(1,\cdot)$
Character field $\Q$
Dimension $260$
Newform subspaces $37$
Sturm bound $1456$
Trace bound $7$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5577.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 37 \)
Sturm bound: \(1456\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5577))\).

Total New Old
Modular forms 756 260 496
Cusp forms 701 260 441
Eisenstein series 55 0 55

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

\(3\)\(11\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(29\)
\(+\)\(+\)\(-\)\(-\)\(35\)
\(+\)\(-\)\(+\)\(-\)\(36\)
\(+\)\(-\)\(-\)\(+\)\(29\)
\(-\)\(+\)\(+\)\(-\)\(33\)
\(-\)\(+\)\(-\)\(+\)\(33\)
\(-\)\(-\)\(+\)\(+\)\(26\)
\(-\)\(-\)\(-\)\(-\)\(39\)
Plus space\(+\)\(117\)
Minus space\(-\)\(143\)

Trace form

\( 260q + 2q^{2} + 2q^{3} + 260q^{4} + 8q^{5} - 4q^{6} + 4q^{7} - 6q^{8} + 260q^{9} + O(q^{10}) \) \( 260q + 2q^{2} + 2q^{3} + 260q^{4} + 8q^{5} - 4q^{6} + 4q^{7} - 6q^{8} + 260q^{9} - 12q^{10} + 6q^{12} - 4q^{14} - 4q^{15} + 268q^{16} + 12q^{17} + 2q^{18} - 4q^{19} + 16q^{20} + 12q^{21} + 2q^{22} + 8q^{23} - 12q^{24} + 292q^{25} + 2q^{27} + 4q^{28} + 12q^{29} - 16q^{30} - 16q^{31} + 10q^{32} - 2q^{33} - 16q^{34} - 40q^{35} + 260q^{36} + 8q^{37} - 12q^{38} - 20q^{40} + 4q^{41} + 20q^{42} + 4q^{43} + 8q^{44} + 8q^{45} + 32q^{46} - 32q^{47} - 2q^{48} + 276q^{49} + 38q^{50} + 16q^{53} - 4q^{54} + 8q^{55} + 28q^{56} + 20q^{57} - 8q^{58} - 16q^{59} + 20q^{60} + 16q^{61} + 16q^{62} + 4q^{63} + 300q^{64} + 4q^{66} - 24q^{67} + 36q^{68} - 16q^{69} + 48q^{70} - 16q^{71} - 6q^{72} + 40q^{73} + 60q^{74} + 14q^{75} - 20q^{76} - 4q^{77} + 12q^{79} + 72q^{80} + 260q^{81} + 56q^{82} - 40q^{83} + 20q^{84} + 16q^{85} - 12q^{86} + 16q^{87} + 18q^{88} + 56q^{89} - 12q^{90} + 104q^{92} + 48q^{94} - 8q^{95} - 28q^{96} + 16q^{97} + 18q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5577))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 11 13
5577.2.a.a \(1\) \(44.533\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-4\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}-4q^{7}+\cdots\)
5577.2.a.b \(1\) \(44.533\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{4}-2q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
5577.2.a.c \(1\) \(44.533\) \(\Q\) None \(0\) \(-1\) \(-2\) \(3\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{4}-2q^{5}+3q^{7}+q^{9}-q^{11}+\cdots\)
5577.2.a.d \(1\) \(44.533\) \(\Q\) None \(0\) \(-1\) \(2\) \(-3\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{4}+2q^{5}-3q^{7}+q^{9}+q^{11}+\cdots\)
5577.2.a.e \(1\) \(44.533\) \(\Q\) None \(0\) \(-1\) \(2\) \(1\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{4}+2q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
5577.2.a.f \(1\) \(44.533\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
5577.2.a.g \(1\) \(44.533\) \(\Q\) None \(1\) \(1\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-3q^{8}+\cdots\)
5577.2.a.h \(2\) \(44.533\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}+(1-\beta )q^{5}-\beta q^{6}+\cdots\)
5577.2.a.i \(2\) \(44.533\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(4\) \(4\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(2+\beta )q^{5}+\cdots\)
5577.2.a.j \(3\) \(44.533\) 3.3.148.1 None \(-3\) \(3\) \(-4\) \(2\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
5577.2.a.k \(3\) \(44.533\) 3.3.148.1 None \(-1\) \(3\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
5577.2.a.l \(3\) \(44.533\) 3.3.564.1 None \(1\) \(-3\) \(2\) \(-2\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
5577.2.a.m \(4\) \(44.533\) 4.4.8468.1 None \(2\) \(-4\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}-\beta _{3}q^{5}+\cdots\)
5577.2.a.n \(5\) \(44.533\) 5.5.233489.1 None \(-4\) \(5\) \(-4\) \(-3\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5577.2.a.o \(5\) \(44.533\) 5.5.863825.1 None \(-2\) \(-5\) \(2\) \(-9\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
5577.2.a.p \(5\) \(44.533\) 5.5.181057.1 None \(-2\) \(5\) \(-8\) \(-9\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
5577.2.a.q \(5\) \(44.533\) 5.5.503376.1 None \(-1\) \(-5\) \(2\) \(-6\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
5577.2.a.r \(5\) \(44.533\) 5.5.1019601.1 None \(0\) \(-5\) \(-2\) \(7\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+\beta _{3}q^{5}+\cdots\)
5577.2.a.s \(5\) \(44.533\) 5.5.1019601.1 None \(0\) \(-5\) \(2\) \(-7\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2}+\beta _{3})q^{4}-\beta _{3}q^{5}+\cdots\)
5577.2.a.t \(5\) \(44.533\) 5.5.503376.1 None \(1\) \(-5\) \(-2\) \(6\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
5577.2.a.u \(5\) \(44.533\) 5.5.863825.1 None \(2\) \(-5\) \(-2\) \(9\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5577.2.a.v \(5\) \(44.533\) 5.5.181057.1 None \(2\) \(5\) \(8\) \(9\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(2+\beta _{3}+\cdots)q^{5}+\cdots\)
5577.2.a.w \(5\) \(44.533\) 5.5.233489.1 None \(4\) \(5\) \(4\) \(3\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)
5577.2.a.x \(7\) \(44.533\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(7\) \(-6\) \(-6\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
5577.2.a.y \(7\) \(44.533\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(7\) \(6\) \(6\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
5577.2.a.z \(12\) \(44.533\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(-12\) \(4\) \(-12\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
5577.2.a.ba \(12\) \(44.533\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(-12\) \(6\) \(1\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{2}+\beta _{6}+\beta _{9}+\cdots)q^{5}+\cdots\)
5577.2.a.bb \(12\) \(44.533\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(12\) \(6\) \(1\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(\beta _{3}-\beta _{5}+\beta _{11})q^{5}+\cdots\)
5577.2.a.bc \(12\) \(44.533\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(-12\) \(-6\) \(-1\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
5577.2.a.bd \(12\) \(44.533\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(12\) \(-6\) \(-1\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots\)
5577.2.a.be \(12\) \(44.533\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(-12\) \(-4\) \(12\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
5577.2.a.bf \(14\) \(44.533\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-6\) \(14\) \(-12\) \(-12\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{9}+\cdots)q^{5}+\cdots\)
5577.2.a.bg \(14\) \(44.533\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(6\) \(14\) \(12\) \(12\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{9}+\cdots)q^{5}+\cdots\)
5577.2.a.bh \(18\) \(44.533\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-1\) \(-18\) \(6\) \(-1\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(\beta _{5}+\beta _{13}+\cdots)q^{5}+\cdots\)
5577.2.a.bi \(18\) \(44.533\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-1\) \(18\) \(6\) \(-1\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
5577.2.a.bj \(18\) \(44.533\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(1\) \(-18\) \(-6\) \(1\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
5577.2.a.bk \(18\) \(44.533\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(1\) \(18\) \(-6\) \(1\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5577))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5577)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1859))\)\(^{\oplus 2}\)