Properties

Label 8020.2.a
Level 8020
Weight 2
Character orbit a
Rep. character \(\chi_{8020}(1,\cdot)\)
Character field \(\Q\)
Dimension 132
Newforms 6
Sturm bound 2412
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(2412\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8020))\).

Total New Old
Modular forms 1212 132 1080
Cusp forms 1201 132 1069
Eisenstein series 11 0 11

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

\(2\)\(5\)\(401\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(37\)
\(-\)\(+\)\(-\)\(+\)\(29\)
\(-\)\(-\)\(+\)\(+\)\(29\)
\(-\)\(-\)\(-\)\(-\)\(37\)
Plus space\(+\)\(58\)
Minus space\(-\)\(74\)

Trace form

\(132q \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 128q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 128q^{9} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 132q^{25} \) \(\mathstrut -\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut +\mathstrut 32q^{53} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut -\mathstrut 44q^{59} \) \(\mathstrut -\mathstrut 20q^{61} \) \(\mathstrut +\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut -\mathstrut 40q^{73} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 12q^{79} \) \(\mathstrut +\mathstrut 140q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 8q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 28q^{93} \) \(\mathstrut -\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut -\mathstrut 68q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8020))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 401
8020.2.a.a \(1\) \(64.040\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
8020.2.a.b \(2\) \(64.040\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+(-1+\beta )q^{3}-q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
8020.2.a.c \(28\) \(64.040\) None \(0\) \(3\) \(-28\) \(-4\) \(-\) \(+\) \(-\)
8020.2.a.d \(29\) \(64.040\) None \(0\) \(-3\) \(29\) \(-8\) \(-\) \(-\) \(+\)
8020.2.a.e \(35\) \(64.040\) None \(0\) \(-1\) \(-35\) \(6\) \(-\) \(+\) \(+\)
8020.2.a.f \(37\) \(64.040\) None \(0\) \(3\) \(37\) \(4\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8020))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(802))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1604))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4010))\)\(^{\oplus 2}\)