↑

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 $9$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7 19
5054.2.a.a 5054.a 1.a $1$ $40.356$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
5054.2.a.b 5054.a 1.a $1$ $40.356$ \(\Q\) None \(1\) \(0\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
5054.2.a.c 5054.a 1.a $1$ $40.356$ \(\Q\) None \(1\) \(2\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
5054.2.a.d 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+(1-3\beta )q^{5}+\beta q^{6}+\cdots\)
5054.2.a.e 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{13}) \) None \(-2\) \(-1\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
5054.2.a.f 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots\)
5054.2.a.g 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{5}) \) None \(-2\) \(1\) \(-3\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.h 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{17}) \) None \(-2\) \(1\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.i 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{5}) \) None \(-2\) \(3\) \(-4\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
5054.2.a.j 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(-4\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
5054.2.a.k 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(2-3\beta )q^{5}+\cdots\)
5054.2.a.l 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(-3\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.m 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{17}) \) None \(2\) \(-1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.n 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{29}) \) None \(2\) \(-1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.o 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+(1-3\beta )q^{5}+\beta q^{6}+\cdots\)
5054.2.a.p 5054.a 1.a $2$ $40.356$ \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots\)
5054.2.a.q 5054.a 1.a $3$ $40.356$ 3.3.148.1 None \(-3\) \(-2\) \(-1\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.r 5054.a 1.a $3$ $40.356$ 3.3.469.1 None \(-3\) \(1\) \(5\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots\)
5054.2.a.s 5054.a 1.a $3$ $40.356$ \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(-3\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5054.2.a.t 5054.a 1.a $3$ $40.356$ \(\Q(\zeta_{18})^+\) None \(3\) \(-3\) \(-3\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5054.2.a.u 5054.a 1.a $3$ $40.356$ 3.3.148.1 None \(3\) \(2\) \(-1\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.v 5054.a 1.a $4$ $40.356$ \(\Q(\zeta_{20})^+\) None \(-4\) \(-4\) \(2\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
5054.2.a.w 5054.a 1.a $4$ $40.356$ 4.4.151572.1 None \(-4\) \(-1\) \(1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
5054.2.a.x 5054.a 1.a $4$ $40.356$ 4.4.151572.1 None \(4\) \(1\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
5054.2.a.y 5054.a 1.a $4$ $40.356$ \(\Q(\zeta_{20})^+\) None \(4\) \(4\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(-\beta _{2}-\beta _{3})q^{5}+\cdots\)
5054.2.a.z 5054.a 1.a $6$ $40.356$ 6.6.36538000.1 None \(-6\) \(0\) \(-1\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
5054.2.a.ba 5054.a 1.a $6$ $40.356$ 6.6.48952000.1 None \(-6\) \(2\) \(-5\) \(-6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
5054.2.a.bb 5054.a 1.a $6$ $40.356$ 6.6.1528713.1 None \(-6\) \(3\) \(-3\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
5054.2.a.bc 5054.a 1.a $6$ $40.356$ 6.6.1528713.1 None \(6\) \(-3\) \(-3\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
5054.2.a.bd 5054.a 1.a $6$ $40.356$ 6.6.48952000.1 None \(6\) \(-2\) \(-5\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
5054.2.a.be 5054.a 1.a $6$ $40.356$ 6.6.36538000.1 None \(6\) \(0\) \(-1\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
5054.2.a.bf 5054.a 1.a $8$ $40.356$ 8.8.\(\cdots\).1 None \(-8\) \(-4\) \(6\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{5}+\beta _{7})q^{3}+q^{4}+(1+\cdots)q^{5}+\cdots\)
5054.2.a.bg 5054.a 1.a $8$ $40.356$ 8.8.\(\cdots\).1 None \(-8\) \(4\) \(-2\) \(8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{2}+\beta _{5})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.bh 5054.a 1.a $8$ $40.356$ 8.8.\(\cdots\).1 None \(8\) \(-4\) \(-2\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{2}-\beta _{5})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.bi 5054.a 1.a $8$ $40.356$ 8.8.\(\cdots\).1 None \(8\) \(4\) \(6\) \(-8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{5}-\beta _{7})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.bj 5054.a 1.a $9$ $40.356$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-3\) \(3\) \(-9\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
5054.2.a.bk 5054.a 1.a $9$ $40.356$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(3\) \(3\) \(-9\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
5054.2.a.bl 5054.a 1.a $12$ $40.356$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-3\) \(3\) \(12\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)
5054.2.a.bm 5054.a 1.a $12$ $40.356$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(3\) \(3\) \(12\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)

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

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