Properties

Label 8010.2.a
Level $8010$
Weight $2$
Character orbit 8010.a
Rep. character $\chi_{8010}(1,\cdot)$
Character field $\Q$
Dimension $144$
Newform subspaces $44$
Sturm bound $3240$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 8010 = 2 \cdot 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8010.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 44 \)
Sturm bound: \(3240\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8010))\).

Total New Old
Modular forms 1636 144 1492
Cusp forms 1605 144 1461
Eisenstein series 31 0 31

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

\(2\)\(3\)\(5\)\(89\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(10\)
\(+\)\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(+\)\(-\)\(+\)$-$\(8\)
\(+\)\(+\)\(-\)\(-\)$+$\(6\)
\(+\)\(-\)\(+\)\(+\)$-$\(11\)
\(+\)\(-\)\(+\)\(-\)$+$\(11\)
\(+\)\(-\)\(-\)\(+\)$+$\(9\)
\(+\)\(-\)\(-\)\(-\)$-$\(13\)
\(-\)\(+\)\(+\)\(+\)$-$\(6\)
\(-\)\(+\)\(+\)\(-\)$+$\(8\)
\(-\)\(+\)\(-\)\(+\)$+$\(4\)
\(-\)\(+\)\(-\)\(-\)$-$\(10\)
\(-\)\(-\)\(+\)\(+\)$+$\(10\)
\(-\)\(-\)\(+\)\(-\)$-$\(12\)
\(-\)\(-\)\(-\)\(+\)$-$\(14\)
\(-\)\(-\)\(-\)\(-\)$+$\(8\)
Plus space\(+\)\(66\)
Minus space\(-\)\(78\)

Trace form

\( 144 q + 144 q^{4} + O(q^{10}) \) \( 144 q + 144 q^{4} + 12 q^{13} + 8 q^{14} + 144 q^{16} + 16 q^{17} + 8 q^{22} - 16 q^{23} + 144 q^{25} + 8 q^{29} + 8 q^{31} - 24 q^{34} + 4 q^{35} - 28 q^{37} + 4 q^{38} - 8 q^{41} - 4 q^{43} - 8 q^{47} + 128 q^{49} + 12 q^{52} + 32 q^{53} - 8 q^{55} + 8 q^{56} - 12 q^{58} + 8 q^{59} + 40 q^{61} + 8 q^{62} + 144 q^{64} - 16 q^{65} + 16 q^{67} + 16 q^{68} + 4 q^{70} - 16 q^{71} + 24 q^{73} - 24 q^{74} - 24 q^{77} + 8 q^{79} - 8 q^{82} - 4 q^{83} + 32 q^{85} + 8 q^{88} + 32 q^{91} - 16 q^{92} + 8 q^{94} - 8 q^{95} - 40 q^{97} - 16 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8010))\) 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 3 5 89
8010.2.a.a 8010.a 1.a $1$ $63.960$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.b 8010.a 1.a $1$ $63.960$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.c 8010.a 1.a $1$ $63.960$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.d 8010.a 1.a $1$ $63.960$ \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.e 8010.a 1.a $1$ $63.960$ \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.f 8010.a 1.a $1$ $63.960$ \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.g 8010.a 1.a $1$ $63.960$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-3q^{11}+\cdots\)
8010.2.a.h 8010.a 1.a $1$ $63.960$ \(\Q\) None \(1\) \(0\) \(-1\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
8010.2.a.i 8010.a 1.a $1$ $63.960$ \(\Q\) None \(1\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
8010.2.a.j 8010.a 1.a $1$ $63.960$ \(\Q\) None \(1\) \(0\) \(1\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.k 8010.a 1.a $1$ $63.960$ \(\Q\) None \(1\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.l 8010.a 1.a $1$ $63.960$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{16}+\cdots\)
8010.2.a.m 8010.a 1.a $1$ $63.960$ \(\Q\) None \(1\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.n 8010.a 1.a $1$ $63.960$ \(\Q\) None \(1\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.o 8010.a 1.a $2$ $63.960$ \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(-2\) \(-4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.p 8010.a 1.a $2$ $63.960$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.q 8010.a 1.a $2$ $63.960$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(-6\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+(-3+\beta )q^{7}-q^{8}+\cdots\)
8010.2.a.r 8010.a 1.a $2$ $63.960$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+\beta q^{7}-q^{8}-q^{10}+\cdots\)
8010.2.a.s 8010.a 1.a $2$ $63.960$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots\)
8010.2.a.t 8010.a 1.a $2$ $63.960$ \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(2\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.u 8010.a 1.a $2$ $63.960$ \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(2\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.v 8010.a 1.a $2$ $63.960$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+\beta q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.w 8010.a 1.a $2$ $63.960$ \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(2\) \(3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
8010.2.a.x 8010.a 1.a $3$ $63.960$ 3.3.148.1 None \(-3\) \(0\) \(-3\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+(-1-\beta _{1}-2\beta _{2})q^{7}+\cdots\)
8010.2.a.y 8010.a 1.a $3$ $63.960$ 3.3.469.1 None \(-3\) \(0\) \(-3\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-\beta _{1}q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.z 8010.a 1.a $3$ $63.960$ 3.3.148.1 None \(-3\) \(0\) \(3\) \(-6\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+(-2-\beta _{2})q^{7}-q^{8}+\cdots\)
8010.2.a.ba 8010.a 1.a $3$ $63.960$ 3.3.148.1 None \(3\) \(0\) \(-3\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+(-1-\beta _{1})q^{7}+q^{8}+\cdots\)
8010.2.a.bb 8010.a 1.a $3$ $63.960$ 3.3.404.1 None \(3\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
8010.2.a.bc 8010.a 1.a $3$ $63.960$ 3.3.404.1 None \(3\) \(0\) \(3\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+(1+\beta _{1})q^{7}+q^{8}+\cdots\)
8010.2.a.bd 8010.a 1.a $4$ $63.960$ 4.4.47032.1 None \(-4\) \(0\) \(4\) \(3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+(1-\beta _{1})q^{7}-q^{8}+\cdots\)
8010.2.a.be 8010.a 1.a $4$ $63.960$ 4.4.31288.1 None \(4\) \(0\) \(-4\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+(\beta _{1}-\beta _{3})q^{7}+q^{8}+\cdots\)
8010.2.a.bf 8010.a 1.a $5$ $63.960$ 5.5.7736352.1 None \(-5\) \(0\) \(-5\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-\beta _{3}q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.bg 8010.a 1.a $5$ $63.960$ 5.5.15020836.1 None \(-5\) \(0\) \(-5\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+\beta _{2}q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.bh 8010.a 1.a $5$ $63.960$ 5.5.21712324.1 None \(-5\) \(0\) \(5\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+(1-\beta _{3})q^{7}-q^{8}+\cdots\)
8010.2.a.bi 8010.a 1.a $5$ $63.960$ 5.5.1186628.1 None \(-5\) \(0\) \(5\) \(8\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+(1+\beta _{3}+\beta _{4})q^{7}+\cdots\)
8010.2.a.bj 8010.a 1.a $5$ $63.960$ 5.5.2991204.1 None \(5\) \(0\) \(-5\) \(1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-\beta _{2}q^{7}+q^{8}-q^{10}+\cdots\)
8010.2.a.bk 8010.a 1.a $6$ $63.960$ 6.6.63199488.1 None \(-6\) \(0\) \(6\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-\beta _{1}q^{7}-q^{8}-q^{10}+\cdots\)
8010.2.a.bl 8010.a 1.a $6$ $63.960$ 6.6.63199488.1 None \(6\) \(0\) \(-6\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-\beta _{1}q^{7}+q^{8}-q^{10}+\cdots\)
8010.2.a.bm 8010.a 1.a $6$ $63.960$ 6.6.387230992.1 None \(6\) \(0\) \(-6\) \(6\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+(1+\beta _{3}+\beta _{5})q^{7}+\cdots\)
8010.2.a.bn 8010.a 1.a $7$ $63.960$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(0\) \(7\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-\beta _{2}q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.bo 8010.a 1.a $8$ $63.960$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(8\) \(-5\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+(-1-\beta _{5})q^{7}-q^{8}+\cdots\)
8010.2.a.bp 8010.a 1.a $8$ $63.960$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(-8\) \(-5\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+(-1-\beta _{5})q^{7}+q^{8}+\cdots\)
8010.2.a.bq 8010.a 1.a $10$ $63.960$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(0\) \(-10\) \(3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-\beta _{5}q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.br 8010.a 1.a $10$ $63.960$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(0\) \(10\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-\beta _{5}q^{7}+q^{8}+q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8010))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(178))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(267))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(445))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(534))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(801))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(890))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1335))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1602))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2670))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4005))\)\(^{\oplus 2}\)