Properties

Label 8010.2.a
Level 8010
Weight 2
Character orbit a
Rep. character \(\chi_{8010}(1,\cdot)\)
Character field \(\Q\)
Dimension 144
Newforms 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: \(\Q\)
Newforms: \( 44 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8010))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 89
8010.2.a.a \(1\) \(63.960\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.b \(1\) \(63.960\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.c \(1\) \(63.960\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.d \(1\) \(63.960\) \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.e \(1\) \(63.960\) \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.f \(1\) \(63.960\) \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.g \(1\) \(63.960\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-3q^{11}+\cdots\)
8010.2.a.h \(1\) \(63.960\) \(\Q\) None \(1\) \(0\) \(-1\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
8010.2.a.i \(1\) \(63.960\) \(\Q\) None \(1\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
8010.2.a.j \(1\) \(63.960\) \(\Q\) None \(1\) \(0\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.k \(1\) \(63.960\) \(\Q\) None \(1\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.l \(1\) \(63.960\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{16}+\cdots\)
8010.2.a.m \(1\) \(63.960\) \(\Q\) None \(1\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.n \(1\) \(63.960\) \(\Q\) None \(1\) \(0\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.o \(2\) \(63.960\) \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(-2\) \(-4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.p \(2\) \(63.960\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.q \(2\) \(63.960\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(-6\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+(-3+\beta )q^{7}-q^{8}+\cdots\)
8010.2.a.r \(2\) \(63.960\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+\beta q^{7}-q^{8}-q^{10}+\cdots\)
8010.2.a.s \(2\) \(63.960\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots\)
8010.2.a.t \(2\) \(63.960\) \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(2\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.u \(2\) \(63.960\) \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.v \(2\) \(63.960\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+\beta q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.w \(2\) \(63.960\) \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(2\) \(3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
8010.2.a.x \(3\) \(63.960\) 3.3.148.1 None \(-3\) \(0\) \(-3\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+(-1-\beta _{1}-2\beta _{2})q^{7}+\cdots\)
8010.2.a.y \(3\) \(63.960\) 3.3.469.1 None \(-3\) \(0\) \(-3\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-\beta _{1}q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.z \(3\) \(63.960\) 3.3.148.1 None \(-3\) \(0\) \(3\) \(-6\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+(-2-\beta _{2})q^{7}-q^{8}+\cdots\)
8010.2.a.ba \(3\) \(63.960\) 3.3.148.1 None \(3\) \(0\) \(-3\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+(-1-\beta _{1})q^{7}+q^{8}+\cdots\)
8010.2.a.bb \(3\) \(63.960\) 3.3.404.1 None \(3\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
8010.2.a.bc \(3\) \(63.960\) 3.3.404.1 None \(3\) \(0\) \(3\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+(1+\beta _{1})q^{7}+q^{8}+\cdots\)
8010.2.a.bd \(4\) \(63.960\) 4.4.47032.1 None \(-4\) \(0\) \(4\) \(3\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+(1-\beta _{1})q^{7}-q^{8}+\cdots\)
8010.2.a.be \(4\) \(63.960\) 4.4.31288.1 None \(4\) \(0\) \(-4\) \(3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+(\beta _{1}-\beta _{3})q^{7}+q^{8}+\cdots\)
8010.2.a.bf \(5\) \(63.960\) 5.5.7736352.1 None \(-5\) \(0\) \(-5\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-\beta _{3}q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.bg \(5\) \(63.960\) 5.5.15020836.1 None \(-5\) \(0\) \(-5\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}+\beta _{2}q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.bh \(5\) \(63.960\) 5.5.21712324.1 None \(-5\) \(0\) \(5\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+(1-\beta _{3})q^{7}-q^{8}+\cdots\)
8010.2.a.bi \(5\) \(63.960\) 5.5.1186628.1 None \(-5\) \(0\) \(5\) \(8\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+(1+\beta _{3}+\beta _{4})q^{7}+\cdots\)
8010.2.a.bj \(5\) \(63.960\) 5.5.2991204.1 None \(5\) \(0\) \(-5\) \(1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-\beta _{2}q^{7}+q^{8}-q^{10}+\cdots\)
8010.2.a.bk \(6\) \(63.960\) 6.6.63199488.1 None \(-6\) \(0\) \(6\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-\beta _{1}q^{7}-q^{8}-q^{10}+\cdots\)
8010.2.a.bl \(6\) \(63.960\) 6.6.63199488.1 None \(6\) \(0\) \(-6\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-\beta _{1}q^{7}+q^{8}-q^{10}+\cdots\)
8010.2.a.bm \(6\) \(63.960\) 6.6.387230992.1 None \(6\) \(0\) \(-6\) \(6\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+(1+\beta _{3}+\beta _{5})q^{7}+\cdots\)
8010.2.a.bn \(7\) \(63.960\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(0\) \(7\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}-\beta _{2}q^{7}+q^{8}+q^{10}+\cdots\)
8010.2.a.bo \(8\) \(63.960\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(8\) \(-5\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+(-1-\beta _{5})q^{7}-q^{8}+\cdots\)
8010.2.a.bp \(8\) \(63.960\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(-8\) \(-5\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+(-1-\beta _{5})q^{7}+q^{8}+\cdots\)
8010.2.a.bq \(10\) \(63.960\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(0\) \(-10\) \(3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-\beta _{5}q^{7}-q^{8}+q^{10}+\cdots\)
8010.2.a.br \(10\) \(63.960\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(0\) \(10\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}-\beta _{5}q^{7}+q^{8}+q^{10}+\cdots\)

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

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