Properties

Label 4730.2.a
Level 4730
Weight 2
Character orbit a
Rep. character \(\chi_{4730}(1,\cdot)\)
Character field \(\Q\)
Dimension 141
Newforms 32
Sturm bound 1584
Trace bound 7

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Defining parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)
Character field: \(\Q\)
Newforms: \( 32 \)
Sturm bound: \(1584\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4730))\).

Total New Old
Modular forms 800 141 659
Cusp forms 785 141 644
Eisenstein series 15 0 15

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

\(2\)\(5\)\(11\)\(43\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(11\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(10\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(13\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(13\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(51\)
Minus space\(-\)\(90\)

Trace form

\( 141q + q^{2} + 4q^{3} + 141q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 153q^{9} + O(q^{10}) \) \( 141q + q^{2} + 4q^{3} + 141q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 153q^{9} + q^{10} + q^{11} + 4q^{12} + 14q^{13} + 8q^{14} + 4q^{15} + 141q^{16} + 2q^{17} + 13q^{18} + 4q^{19} + q^{20} + 32q^{21} + q^{22} + 8q^{23} + 4q^{24} + 141q^{25} + 14q^{26} + 40q^{27} + 8q^{28} + 14q^{29} + 4q^{30} + 32q^{31} + q^{32} + 4q^{33} + 18q^{34} + 8q^{35} + 153q^{36} + 22q^{37} - 4q^{38} + 8q^{39} + q^{40} + 42q^{41} - 16q^{42} + q^{43} + q^{44} + 13q^{45} + 24q^{46} - 32q^{47} + 4q^{48} + 181q^{49} + q^{50} + 8q^{51} + 14q^{52} - 50q^{53} - 56q^{54} + q^{55} + 8q^{56} - 32q^{57} + 22q^{58} + 12q^{59} + 4q^{60} + 62q^{61} - 32q^{62} - 8q^{63} + 141q^{64} + 14q^{65} + 4q^{66} - 4q^{67} + 2q^{68} + 16q^{69} + 8q^{70} - 8q^{71} + 13q^{72} + 26q^{73} - 26q^{74} + 4q^{75} + 4q^{76} - 8q^{77} - 8q^{78} + 16q^{79} + q^{80} + 197q^{81} + 10q^{82} + 52q^{83} + 32q^{84} + 18q^{85} + q^{86} + 8q^{87} + q^{88} - 22q^{89} + 13q^{90} + 80q^{91} + 8q^{92} + 64q^{93} - 12q^{95} + 4q^{96} + 50q^{97} + 25q^{98} + 13q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4730))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 11 43
4730.2.a.a \(1\) \(37.769\) \(\Q\) None \(-1\) \(-2\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{8}+\cdots\)
4730.2.a.b \(1\) \(37.769\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots\)
4730.2.a.c \(1\) \(37.769\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots\)
4730.2.a.d \(1\) \(37.769\) \(\Q\) None \(1\) \(-3\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}-3q^{3}+q^{4}+q^{5}-3q^{6}+q^{7}+\cdots\)
4730.2.a.e \(1\) \(37.769\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
4730.2.a.f \(1\) \(37.769\) \(\Q\) None \(1\) \(0\) \(-1\) \(3\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-3q^{9}+\cdots\)
4730.2.a.g \(1\) \(37.769\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
4730.2.a.h \(1\) \(37.769\) \(\Q\) None \(1\) \(1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
4730.2.a.i \(1\) \(37.769\) \(\Q\) None \(1\) \(1\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
4730.2.a.j \(1\) \(37.769\) \(\Q\) None \(1\) \(1\) \(1\) \(5\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+5q^{7}+\cdots\)
4730.2.a.k \(1\) \(37.769\) \(\Q\) None \(1\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots\)
4730.2.a.l \(2\) \(37.769\) \(\Q(\sqrt{17}) \) None \(-2\) \(-1\) \(2\) \(-6\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-3q^{7}+\cdots\)
4730.2.a.m \(2\) \(37.769\) \(\Q(\sqrt{17}) \) None \(-2\) \(-1\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-2\beta q^{7}+\cdots\)
4730.2.a.n \(2\) \(37.769\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)
4730.2.a.o \(2\) \(37.769\) \(\Q(\sqrt{13}) \) None \(-2\) \(1\) \(-2\) \(-1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)
4730.2.a.p \(2\) \(37.769\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
4730.2.a.q \(2\) \(37.769\) \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(2\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
4730.2.a.r \(2\) \(37.769\) \(\Q(\sqrt{21}) \) None \(2\) \(1\) \(-2\) \(-5\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
4730.2.a.s \(2\) \(37.769\) \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(2\) \(-5\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
4730.2.a.t \(3\) \(37.769\) 3.3.1373.1 None \(-3\) \(0\) \(3\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
4730.2.a.u \(4\) \(37.769\) 4.4.23252.1 None \(4\) \(-3\) \(4\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
4730.2.a.v \(5\) \(37.769\) 5.5.220036.1 None \(5\) \(2\) \(-5\) \(-6\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
4730.2.a.w \(8\) \(37.769\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-7\) \(8\) \(-6\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
4730.2.a.x \(8\) \(37.769\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(-8\) \(-5\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
4730.2.a.y \(8\) \(37.769\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(3\) \(8\) \(11\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
4730.2.a.z \(10\) \(37.769\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(8\) \(10\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
4730.2.a.ba \(10\) \(37.769\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-1\) \(-10\) \(3\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
4730.2.a.bb \(11\) \(37.769\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(-1\) \(-11\) \(6\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
4730.2.a.bc \(11\) \(37.769\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(0\) \(-11\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
4730.2.a.bd \(11\) \(37.769\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(11\) \(3\) \(11\) \(5\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
4730.2.a.be \(12\) \(37.769\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(3\) \(12\) \(8\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
4730.2.a.bf \(13\) \(37.769\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(13\) \(0\) \(-13\) \(7\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4730))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4730)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(430))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(473))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(946))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2365))\)\(^{\oplus 2}\)