Properties

Label 5054.2.a
Level $5054$
Weight $2$
Character orbit 5054.a
Rep. character $\chi_{5054}(1,\cdot)$
Character field $\Q$
Dimension $170$
Newform subspaces $39$
Sturm bound $1520$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5054.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 39 \)
Sturm bound: \(1520\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5054))\).

Total New Old
Modular forms 800 170 630
Cusp forms 721 170 551
Eisenstein series 79 0 79

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

\(2\)\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(18\)
\(+\)\(+\)\(-\)\(-\)\(25\)
\(+\)\(-\)\(+\)\(-\)\(26\)
\(+\)\(-\)\(-\)\(+\)\(16\)
\(-\)\(+\)\(+\)\(-\)\(22\)
\(-\)\(+\)\(-\)\(+\)\(20\)
\(-\)\(-\)\(+\)\(+\)\(14\)
\(-\)\(-\)\(-\)\(-\)\(29\)
Plus space\(+\)\(68\)
Minus space\(-\)\(102\)

Trace form

\( 170q - 2q^{3} + 170q^{4} - 6q^{5} + 2q^{6} + 162q^{9} + O(q^{10}) \) \( 170q - 2q^{3} + 170q^{4} - 6q^{5} + 2q^{6} + 162q^{9} - 6q^{10} - 8q^{11} - 2q^{12} - 2q^{13} + 2q^{14} + 170q^{16} + 4q^{18} - 6q^{20} - 2q^{21} + 12q^{22} + 8q^{23} + 2q^{24} + 166q^{25} - 2q^{26} + 4q^{27} + 16q^{29} + 16q^{30} - 28q^{31} + 24q^{33} - 12q^{34} + 2q^{35} + 162q^{36} - 16q^{37} + 16q^{39} - 6q^{40} + 8q^{41} - 2q^{42} - 8q^{44} + 18q^{45} + 36q^{47} - 2q^{48} + 170q^{49} + 12q^{50} + 44q^{51} - 2q^{52} + 20q^{53} + 44q^{54} + 32q^{55} + 2q^{56} + 26q^{59} - 6q^{61} + 20q^{62} + 12q^{63} + 170q^{64} + 52q^{65} + 32q^{66} + 8q^{67} + 32q^{69} + 6q^{70} + 4q^{72} - 4q^{73} - 14q^{75} + 4q^{77} - 40q^{79} - 6q^{80} + 174q^{81} + 12q^{82} + 26q^{83} - 2q^{84} - 4q^{85} + 20q^{86} + 36q^{87} + 12q^{88} - 28q^{89} - 6q^{90} - 14q^{91} + 8q^{92} + 8q^{93} - 20q^{94} + 2q^{96} - 32q^{97} - 56q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5054))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 19
5054.2.a.a \(1\) \(40.356\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
5054.2.a.b \(1\) \(40.356\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
5054.2.a.c \(1\) \(40.356\) \(\Q\) None \(1\) \(2\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
5054.2.a.d \(2\) \(40.356\) \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta q^{3}+q^{4}+(1-3\beta )q^{5}+\beta q^{6}+\cdots\)
5054.2.a.e \(2\) \(40.356\) \(\Q(\sqrt{13}) \) None \(-2\) \(-1\) \(1\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
5054.2.a.f \(2\) \(40.356\) \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots\)
5054.2.a.g \(2\) \(40.356\) \(\Q(\sqrt{5}) \) None \(-2\) \(1\) \(-3\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.h \(2\) \(40.356\) \(\Q(\sqrt{17}) \) None \(-2\) \(1\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.i \(2\) \(40.356\) \(\Q(\sqrt{5}) \) None \(-2\) \(3\) \(-4\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
5054.2.a.j \(2\) \(40.356\) \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(-4\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
5054.2.a.k \(2\) \(40.356\) \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(1\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(2-3\beta )q^{5}+\cdots\)
5054.2.a.l \(2\) \(40.356\) \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(-3\) \(2\) \(-\) \(-\) \(+\) \(q+q^{2}-\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.m \(2\) \(40.356\) \(\Q(\sqrt{17}) \) None \(2\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.n \(2\) \(40.356\) \(\Q(\sqrt{29}) \) None \(2\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.o \(2\) \(40.356\) \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta q^{3}+q^{4}+(1-3\beta )q^{5}+\beta q^{6}+\cdots\)
5054.2.a.p \(2\) \(40.356\) \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots\)
5054.2.a.q \(3\) \(40.356\) 3.3.148.1 None \(-3\) \(-2\) \(-1\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.r \(3\) \(40.356\) 3.3.469.1 None \(-3\) \(1\) \(5\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots\)
5054.2.a.s \(3\) \(40.356\) \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(-3\) \(3\) \(+\) \(-\) \(-\) \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5054.2.a.t \(3\) \(40.356\) \(\Q(\zeta_{18})^+\) None \(3\) \(-3\) \(-3\) \(3\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5054.2.a.u \(3\) \(40.356\) 3.3.148.1 None \(3\) \(2\) \(-1\) \(-3\) \(-\) \(+\) \(+\) \(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.v \(4\) \(40.356\) \(\Q(\zeta_{20})^+\) None \(-4\) \(-4\) \(2\) \(4\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
5054.2.a.w \(4\) \(40.356\) 4.4.151572.1 None \(-4\) \(-1\) \(1\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
5054.2.a.x \(4\) \(40.356\) 4.4.151572.1 None \(4\) \(1\) \(1\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
5054.2.a.y \(4\) \(40.356\) \(\Q(\zeta_{20})^+\) None \(4\) \(4\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(-\beta _{2}-\beta _{3})q^{5}+\cdots\)
5054.2.a.z \(6\) \(40.356\) 6.6.36538000.1 None \(-6\) \(0\) \(-1\) \(6\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
5054.2.a.ba \(6\) \(40.356\) 6.6.48952000.1 None \(-6\) \(2\) \(-5\) \(-6\) \(+\) \(+\) \(-\) \(q-q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
5054.2.a.bb \(6\) \(40.356\) 6.6.1528713.1 None \(-6\) \(3\) \(-3\) \(-6\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta _{3}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
5054.2.a.bc \(6\) \(40.356\) 6.6.1528713.1 None \(6\) \(-3\) \(-3\) \(-6\) \(-\) \(+\) \(-\) \(q+q^{2}-\beta _{3}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
5054.2.a.bd \(6\) \(40.356\) 6.6.48952000.1 None \(6\) \(-2\) \(-5\) \(-6\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
5054.2.a.be \(6\) \(40.356\) 6.6.36538000.1 None \(6\) \(0\) \(-1\) \(6\) \(-\) \(-\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
5054.2.a.bf \(8\) \(40.356\) 8.8.\(\cdots\).1 None \(-8\) \(-4\) \(6\) \(-8\) \(+\) \(+\) \(+\) \(q-q^{2}+(-1-\beta _{5}+\beta _{7})q^{3}+q^{4}+(1+\cdots)q^{5}+\cdots\)
5054.2.a.bg \(8\) \(40.356\) 8.8.\(\cdots\).1 None \(-8\) \(4\) \(-2\) \(8\) \(+\) \(-\) \(+\) \(q-q^{2}+(1+\beta _{2}+\beta _{5})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.bh \(8\) \(40.356\) 8.8.\(\cdots\).1 None \(8\) \(-4\) \(-2\) \(8\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1-\beta _{2}-\beta _{5})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.bi \(8\) \(40.356\) 8.8.\(\cdots\).1 None \(8\) \(4\) \(6\) \(-8\) \(-\) \(+\) \(+\) \(q+q^{2}+(1+\beta _{5}-\beta _{7})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.bj \(9\) \(40.356\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-3\) \(3\) \(-9\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
5054.2.a.bk \(9\) \(40.356\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(3\) \(3\) \(-9\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
5054.2.a.bl \(12\) \(40.356\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-3\) \(3\) \(12\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)
5054.2.a.bm \(12\) \(40.356\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(3\) \(3\) \(12\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5054))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5054)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2527))\)\(^{\oplus 2}\)