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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5290))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 23
5290.2.a.a \(1\) \(42.241\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(2\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
5290.2.a.b \(1\) \(42.241\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
5290.2.a.c \(1\) \(42.241\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
5290.2.a.d \(1\) \(42.241\) \(\Q\) None \(-1\) \(1\) \(1\) \(4\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
5290.2.a.e \(2\) \(42.241\) \(\Q(\sqrt{21}) \) None \(-2\) \(-1\) \(2\) \(-1\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.f \(2\) \(42.241\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.g \(2\) \(42.241\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
5290.2.a.h \(2\) \(42.241\) \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(-2\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.i \(2\) \(42.241\) \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(2\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
5290.2.a.j \(2\) \(42.241\) \(\Q(\sqrt{13}) \) None \(-2\) \(3\) \(-2\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.k \(2\) \(42.241\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.l \(2\) \(42.241\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.m \(2\) \(42.241\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.n \(2\) \(42.241\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
5290.2.a.o \(2\) \(42.241\) \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(-2\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5290.2.a.p \(3\) \(42.241\) 3.3.1509.1 None \(3\) \(-1\) \(-3\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
5290.2.a.q \(3\) \(42.241\) 3.3.1509.1 None \(3\) \(-1\) \(3\) \(3\) \(-\) \(-\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
5290.2.a.r \(3\) \(42.241\) 3.3.1101.1 None \(3\) \(1\) \(3\) \(-3\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.s \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(-4\) \(-4\) \(-4\) \(-8\) \(+\) \(+\) \(+\) \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.t \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(-4\) \(-4\) \(4\) \(8\) \(+\) \(-\) \(+\) \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.u \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(-4\) \(4\) \(-4\) \(4\) \(+\) \(+\) \(+\) \(q-q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.v \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(-4\) \(4\) \(4\) \(-4\) \(+\) \(-\) \(+\) \(q-q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.w \(4\) \(42.241\) 4.4.13888.1 None \(4\) \(-2\) \(-4\) \(2\) \(-\) \(+\) \(+\) \(q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.x \(4\) \(42.241\) 4.4.13888.1 None \(4\) \(-2\) \(4\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.y \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(4\) \(0\) \(-4\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.z \(4\) \(42.241\) \(\Q(\zeta_{24})^+\) None \(4\) \(0\) \(4\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.ba \(4\) \(42.241\) 4.4.4752.1 None \(4\) \(2\) \(-4\) \(-6\) \(-\) \(+\) \(-\) \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}-q^{5}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
5290.2.a.bb \(4\) \(42.241\) 4.4.4752.1 None \(4\) \(2\) \(4\) \(6\) \(-\) \(-\) \(-\) \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+q^{5}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
5290.2.a.bc \(5\) \(42.241\) \(\Q(\zeta_{22})^+\) None \(5\) \(-4\) \(-5\) \(2\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.bd \(5\) \(42.241\) \(\Q(\zeta_{22})^+\) None \(5\) \(-4\) \(5\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
5290.2.a.be \(6\) \(42.241\) 6.6.252973568.1 None \(-6\) \(-2\) \(-6\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.bf \(6\) \(42.241\) 6.6.252973568.1 None \(-6\) \(-2\) \(6\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.bg \(10\) \(42.241\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-5\) \(-10\) \(5\) \(+\) \(+\) \(+\) \(q-q^{2}+(-1-\beta _{7})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
5290.2.a.bh \(10\) \(42.241\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-5\) \(10\) \(-5\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1-\beta _{7})q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
5290.2.a.bi \(10\) \(42.241\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(4\) \(-10\) \(7\) \(+\) \(+\) \(-\) \(q-q^{2}+(1+\beta _{7}+\beta _{9})q^{3}+q^{4}-q^{5}+\cdots\)
5290.2.a.bj \(10\) \(42.241\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(4\) \(10\) \(-7\) \(+\) \(-\) \(+\) \(q-q^{2}+(1+\beta _{7}+\beta _{9})q^{3}+q^{4}+q^{5}+\cdots\)
5290.2.a.bk \(15\) \(42.241\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(5\) \(-15\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5290.2.a.bl \(15\) \(42.241\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(15\) \(5\) \(15\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

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

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