Properties

Label 570.6.a
Level $570$
Weight $6$
Character orbit 570.a
Rep. character $\chi_{570}(1,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $17$
Sturm bound $720$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 570.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(720\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(570))\).

Total New Old
Modular forms 608 60 548
Cusp forms 592 60 532
Eisenstein series 16 0 16

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

\(2\)\(3\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(26\)
Minus space\(-\)\(34\)

Trace form

\( 60q + 960q^{4} + 4860q^{9} + O(q^{10}) \) \( 60q + 960q^{4} + 4860q^{9} - 1424q^{11} + 1616q^{13} + 15360q^{16} + 5776q^{17} + 7216q^{23} + 37500q^{25} - 12080q^{29} - 3600q^{30} - 21848q^{31} - 4464q^{33} + 1760q^{34} + 12400q^{35} + 77760q^{36} + 12496q^{37} + 11160q^{39} - 16848q^{41} - 14112q^{42} - 15544q^{43} - 22784q^{44} + 18336q^{46} - 58496q^{47} + 118012q^{49} + 56592q^{51} + 25856q^{52} - 13376q^{53} + 35400q^{55} - 12996q^{57} + 10432q^{58} + 104544q^{59} + 135800q^{61} - 17984q^{62} + 245760q^{64} + 400q^{65} + 39168q^{66} + 53536q^{67} + 92416q^{68} + 39456q^{69} - 48096q^{71} - 171336q^{73} - 73152q^{74} + 119152q^{77} + 110016q^{78} + 403352q^{79} + 393660q^{81} - 17824q^{82} - 110272q^{83} - 65400q^{85} - 214848q^{86} + 120672q^{87} + 532224q^{89} + 614736q^{91} + 115456q^{92} + 17136q^{93} + 35872q^{94} + 39584q^{97} + 477184q^{98} - 115344q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(570))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 19
570.6.a.a \(1\) \(91.419\) \(\Q\) None \(-4\) \(9\) \(-25\) \(-82\) \(+\) \(-\) \(+\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-5^{2}q^{5}-6^{2}q^{6}+\cdots\)
570.6.a.b \(2\) \(91.419\) \(\Q(\sqrt{273}) \) None \(-8\) \(18\) \(-50\) \(-88\) \(+\) \(-\) \(+\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-5^{2}q^{5}-6^{2}q^{6}+\cdots\)
570.6.a.c \(2\) \(91.419\) \(\Q(\sqrt{139}) \) None \(8\) \(18\) \(50\) \(-222\) \(-\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+5^{2}q^{5}+6^{2}q^{6}+\cdots\)
570.6.a.d \(3\) \(91.419\) 3.3.237212.1 None \(-12\) \(-27\) \(75\) \(-10\) \(+\) \(+\) \(-\) \(+\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+5^{2}q^{5}+6^{2}q^{6}+\cdots\)
570.6.a.e \(3\) \(91.419\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(12\) \(-27\) \(-75\) \(10\) \(-\) \(+\) \(+\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-5^{2}q^{5}-6^{2}q^{6}+\cdots\)
570.6.a.f \(3\) \(91.419\) 3.3.838140.1 None \(12\) \(-27\) \(75\) \(-10\) \(-\) \(+\) \(-\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+5^{2}q^{5}-6^{2}q^{6}+\cdots\)
570.6.a.g \(3\) \(91.419\) 3.3.2179928.1 None \(12\) \(27\) \(-75\) \(-170\) \(-\) \(-\) \(+\) \(+\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}-5^{2}q^{5}+6^{2}q^{6}+\cdots\)
570.6.a.h \(4\) \(91.419\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-16\) \(-36\) \(-100\) \(-88\) \(+\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}-5^{2}q^{5}+6^{2}q^{6}+\cdots\)
570.6.a.i \(4\) \(91.419\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-16\) \(-36\) \(-100\) \(108\) \(+\) \(+\) \(+\) \(+\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}-5^{2}q^{5}+6^{2}q^{6}+\cdots\)
570.6.a.j \(4\) \(91.419\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-16\) \(-36\) \(100\) \(-108\) \(+\) \(+\) \(-\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+5^{2}q^{5}+6^{2}q^{6}+\cdots\)
570.6.a.k \(4\) \(91.419\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-16\) \(36\) \(-100\) \(26\) \(+\) \(-\) \(+\) \(+\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-5^{2}q^{5}-6^{2}q^{6}+\cdots\)
570.6.a.l \(4\) \(91.419\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-16\) \(36\) \(100\) \(-26\) \(+\) \(-\) \(-\) \(+\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+5^{2}q^{5}-6^{2}q^{6}+\cdots\)
570.6.a.m \(4\) \(91.419\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-16\) \(36\) \(100\) \(268\) \(+\) \(-\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+5^{2}q^{5}-6^{2}q^{6}+\cdots\)
570.6.a.n \(4\) \(91.419\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(16\) \(-36\) \(-100\) \(10\) \(-\) \(+\) \(+\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-5^{2}q^{5}-6^{2}q^{6}+\cdots\)
570.6.a.o \(5\) \(91.419\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(-45\) \(125\) \(88\) \(-\) \(+\) \(-\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+5^{2}q^{5}-6^{2}q^{6}+\cdots\)
570.6.a.p \(5\) \(91.419\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(45\) \(-125\) \(26\) \(-\) \(-\) \(+\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}-5^{2}q^{5}+6^{2}q^{6}+\cdots\)
570.6.a.q \(5\) \(91.419\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(45\) \(125\) \(268\) \(-\) \(-\) \(-\) \(+\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+5^{2}q^{5}+6^{2}q^{6}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(570))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(570)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 2}\)