Properties

Label 8040.2.a
Level 8040
Weight 2
Character orbit a
Rep. character \(\chi_{8040}(1,\cdot)\)
Character field \(\Q\)
Dimension 132
Newforms 29
Sturm bound 3264
Trace bound 11

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Defining parameters

Level: \( N \) = \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8040.a (trivial)
Character field: \(\Q\)
Newforms: \( 29 \)
Sturm bound: \(3264\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8040))\).

Total New Old
Modular forms 1648 132 1516
Cusp forms 1617 132 1485
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.

\(2\)\(3\)\(5\)\(67\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(11\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(58\)
Minus space\(-\)\(74\)

Trace form

\(132q \) \(\mathstrut +\mathstrut 132q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 132q^{9} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 132q^{25} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 24q^{37} \) \(\mathstrut -\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 124q^{49} \) \(\mathstrut +\mathstrut 16q^{53} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 132q^{81} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 40q^{89} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 8q^{93} \) \(\mathstrut -\mathstrut 16q^{97} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8040))\) 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 67
8040.2.a.a \(1\) \(64.200\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
8040.2.a.b \(1\) \(64.200\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{9}+2q^{13}+q^{15}+2q^{17}+\cdots\)
8040.2.a.c \(1\) \(64.200\) \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8040.2.a.d \(1\) \(64.200\) \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
8040.2.a.e \(1\) \(64.200\) \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-2q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
8040.2.a.f \(1\) \(64.200\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
8040.2.a.g \(1\) \(64.200\) \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8040.2.a.h \(1\) \(64.200\) \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-2q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
8040.2.a.i \(1\) \(64.200\) \(\Q\) None \(0\) \(1\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
8040.2.a.j \(1\) \(64.200\) \(\Q\) None \(0\) \(1\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
8040.2.a.k \(1\) \(64.200\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
8040.2.a.l \(1\) \(64.200\) \(\Q\) None \(0\) \(1\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+4q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
8040.2.a.m \(2\) \(64.200\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
8040.2.a.n \(5\) \(64.200\) 5.5.1034533.1 None \(0\) \(-5\) \(-5\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(-\beta _{1}-\beta _{4})q^{7}+q^{9}+\cdots\)
8040.2.a.o \(5\) \(64.200\) 5.5.630757.1 None \(0\) \(-5\) \(5\) \(6\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(1-\beta _{3})q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
8040.2.a.p \(5\) \(64.200\) 5.5.81589.1 None \(0\) \(5\) \(5\) \(-7\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+(-1-\beta _{3}-\beta _{4})q^{7}+q^{9}+\cdots\)
8040.2.a.q \(6\) \(64.200\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-6\) \(6\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+(-1-\beta _{4}+\cdots)q^{11}+\cdots\)
8040.2.a.r \(6\) \(64.200\) 6.6.15350572.1 None \(0\) \(6\) \(-6\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-1+\beta _{4})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
8040.2.a.s \(6\) \(64.200\) 6.6.24199421.1 None \(0\) \(6\) \(6\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+\beta _{4}q^{7}+q^{9}+(-\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots\)
8040.2.a.t \(7\) \(64.200\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(7\) \(-7\) \(10\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(1+\beta _{3})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
8040.2.a.u \(8\) \(64.200\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-8\) \(-8\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-\beta _{4}q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
8040.2.a.v \(8\) \(64.200\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-8\) \(8\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-\beta _{7}q^{7}+q^{9}+(1+\beta _{4}+\cdots)q^{11}+\cdots\)
8040.2.a.w \(8\) \(64.200\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(-8\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+\beta _{4}q^{7}+q^{9}+(1-\beta _{3}+\cdots)q^{11}+\cdots\)
8040.2.a.x \(8\) \(64.200\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(8\) \(5\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+(1-\beta _{1})q^{7}+q^{9}-\beta _{4}q^{11}+\cdots\)
8040.2.a.y \(9\) \(64.200\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(-9\) \(-6\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(-1-\beta _{6})q^{7}+q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
8040.2.a.z \(9\) \(64.200\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(-9\) \(4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+\beta _{2}q^{7}+q^{9}-\beta _{4}q^{11}+\cdots\)
8040.2.a.ba \(9\) \(64.200\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(9\) \(-9\) \(-7\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
8040.2.a.bb \(9\) \(64.200\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(9\) \(9\) \(5\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8040.2.a.bc \(10\) \(64.200\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-10\) \(10\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-\beta _{9}q^{7}+q^{9}+(1-\beta _{7}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(201))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(268))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(335))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(402))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(536))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(670))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(804))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1005))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1340))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2010))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4020))\)\(^{\oplus 2}\)