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Properties

Label 5290.2.a
Level $5290$
Weight $2$
Character orbit 5290.a
Rep. character $\chi_{5290}(1,\cdot)$
Character field $\Q$
Dimension $167$
Newform subspaces $38$
Sturm bound $1656$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(1656\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5290))\).

Total New Old
Modular forms 876 167 709
Cusp forms 781 167 614
Eisenstein series 95 0 95

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

\(2\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)$+$\(24\)
\(+\)\(+\)\(-\)$-$\(18\)
\(+\)\(-\)\(+\)$-$\(24\)
\(+\)\(-\)\(-\)$+$\(18\)
\(-\)\(+\)\(+\)$-$\(23\)
\(-\)\(+\)\(-\)$+$\(18\)
\(-\)\(-\)\(+\)$+$\(13\)
\(-\)\(-\)\(-\)$-$\(29\)
Plus space\(+\)\(73\)
Minus space\(-\)\(94\)

Trace form

\( 167 q - q^{2} - 4 q^{3} + 167 q^{4} + q^{5} - 8 q^{7} - q^{8} + 159 q^{9} + O(q^{10}) \) \( 167 q - q^{2} - 4 q^{3} + 167 q^{4} + q^{5} - 8 q^{7} - q^{8} + 159 q^{9} + q^{10} - 4 q^{12} - 6 q^{13} - 4 q^{15} + 167 q^{16} + 6 q^{17} + 3 q^{18} - 8 q^{19} + q^{20} + 16 q^{21} - 8 q^{22} + 167 q^{25} + 14 q^{26} + 8 q^{27} - 8 q^{28} + 14 q^{29} + 4 q^{30} - q^{32} + 24 q^{33} + 6 q^{34} + 4 q^{35} + 159 q^{36} - 10 q^{37} + 8 q^{38} + 16 q^{39} + q^{40} + 30 q^{41} + 32 q^{42} - 24 q^{43} + 13 q^{45} + 24 q^{47} - 4 q^{48} + 167 q^{49} - q^{50} + 32 q^{51} - 6 q^{52} + 22 q^{53} + 24 q^{54} + 12 q^{55} + 48 q^{57} + 26 q^{58} + 32 q^{59} - 4 q^{60} - 10 q^{61} + 16 q^{63} + 167 q^{64} + 6 q^{65} + 8 q^{66} - 24 q^{67} + 6 q^{68} + 4 q^{70} + 16 q^{71} + 3 q^{72} - 2 q^{73} + 6 q^{74} - 4 q^{75} - 8 q^{76} + 8 q^{77} - 16 q^{78} - 24 q^{79} + q^{80} + 143 q^{81} - 10 q^{82} - 8 q^{83} + 16 q^{84} - 10 q^{85} - 24 q^{86} - 16 q^{87} - 8 q^{88} - 18 q^{89} + 13 q^{90} - 16 q^{91} - 40 q^{93} - 8 q^{94} + 12 q^{95} - 10 q^{97} - 25 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5290))\) 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 5 23
5290.2.a.a 5290.a 1.a $1$ $42.241$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
5290.2.a.b 5290.a 1.a $1$ $42.241$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5290.2.a.c 5290.a 1.a $1$ $42.241$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
5290.2.a.d 5290.a 1.a $1$ $42.241$ \(\Q\) None \(-1\) \(1\) \(1\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
5290.2.a.e 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{21}) \) None \(-2\) \(-1\) \(2\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.f 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.g 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
5290.2.a.h 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(-2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.i 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
5290.2.a.j 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{13}) \) None \(-2\) \(3\) \(-2\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.k 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.l 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.m 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.n 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
5290.2.a.o 5290.a 1.a $2$ $42.241$ \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(-2\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.p 5290.a 1.a $3$ $42.241$ 3.3.1509.1 None \(3\) \(-1\) \(-3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
5290.2.a.q 5290.a 1.a $3$ $42.241$ 3.3.1509.1 None \(3\) \(-1\) \(3\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
5290.2.a.r 5290.a 1.a $3$ $42.241$ 3.3.1101.1 None \(3\) \(1\) \(3\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.s 5290.a 1.a $4$ $42.241$ \(\Q(\zeta_{24})^+\) None \(-4\) \(-4\) \(-4\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.t 5290.a 1.a $4$ $42.241$ \(\Q(\zeta_{24})^+\) None \(-4\) \(-4\) \(4\) \(8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.u 5290.a 1.a $4$ $42.241$ \(\Q(\zeta_{24})^+\) None \(-4\) \(4\) \(-4\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.v 5290.a 1.a $4$ $42.241$ \(\Q(\zeta_{24})^+\) None \(-4\) \(4\) \(4\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.w 5290.a 1.a $4$ $42.241$ 4.4.13888.1 None \(4\) \(-2\) \(-4\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.x 5290.a 1.a $4$ $42.241$ 4.4.13888.1 None \(4\) \(-2\) \(4\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.y 5290.a 1.a $4$ $42.241$ \(\Q(\zeta_{24})^+\) None \(4\) \(0\) \(-4\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.z 5290.a 1.a $4$ $42.241$ \(\Q(\zeta_{24})^+\) None \(4\) \(0\) \(4\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.ba 5290.a 1.a $4$ $42.241$ 4.4.4752.1 None \(4\) \(2\) \(-4\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}-q^{5}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
5290.2.a.bb 5290.a 1.a $4$ $42.241$ 4.4.4752.1 None \(4\) \(2\) \(4\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+q^{5}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
5290.2.a.bc 5290.a 1.a $5$ $42.241$ \(\Q(\zeta_{22})^+\) None \(5\) \(-4\) \(-5\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.bd 5290.a 1.a $5$ $42.241$ \(\Q(\zeta_{22})^+\) None \(5\) \(-4\) \(5\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.be 5290.a 1.a $6$ $42.241$ 6.6.252973568.1 None \(-6\) \(-2\) \(-6\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.bf 5290.a 1.a $6$ $42.241$ 6.6.252973568.1 None \(-6\) \(-2\) \(6\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.bg 5290.a 1.a $10$ $42.241$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-5\) \(-10\) \(5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{7})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
5290.2.a.bh 5290.a 1.a $10$ $42.241$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-5\) \(10\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{7})q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
5290.2.a.bi 5290.a 1.a $10$ $42.241$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(4\) \(-10\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{7}+\beta _{9})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.bj 5290.a 1.a $10$ $42.241$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(4\) \(10\) \(-7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{7}+\beta _{9})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.bk 5290.a 1.a $15$ $42.241$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(5\) \(-15\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.bl 5290.a 1.a $15$ $42.241$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(5\) \(15\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5290))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5290)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2645))\)\(^{\oplus 2}\)