Properties

Label 8019.2.a
Level 8019
Weight 2
Character orbit a
Rep. character \(\chi_{8019}(1,\cdot)\)
Character field \(\Q\)
Dimension 360
Newforms 12
Sturm bound 1944
Trace bound 5

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Defining parameters

Level: \( N \) = \( 8019 = 3^{6} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8019.a (trivial)
Character field: \(\Q\)
Newforms: \( 12 \)
Sturm bound: \(1944\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8019))\).

Total New Old
Modular forms 1008 360 648
Cusp forms 937 360 577
Eisenstein series 71 0 71

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

\(3\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(87\)
\(+\)\(-\)\(-\)\(99\)
\(-\)\(+\)\(-\)\(93\)
\(-\)\(-\)\(+\)\(81\)
Plus space\(+\)\(168\)
Minus space\(-\)\(192\)

Trace form

\(360q \) \(\mathstrut +\mathstrut 360q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(360q \) \(\mathstrut +\mathstrut 360q^{4} \) \(\mathstrut +\mathstrut 360q^{16} \) \(\mathstrut +\mathstrut 360q^{25} \) \(\mathstrut +\mathstrut 360q^{49} \) \(\mathstrut -\mathstrut 36q^{61} \) \(\mathstrut +\mathstrut 360q^{64} \) \(\mathstrut -\mathstrut 36q^{67} \) \(\mathstrut -\mathstrut 36q^{73} \) \(\mathstrut +\mathstrut 108q^{82} \) \(\mathstrut +\mathstrut 108q^{85} \) \(\mathstrut -\mathstrut 36q^{91} \) \(\mathstrut +\mathstrut 108q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 11
8019.2.a.a \(3\) \(64.032\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(-3\) \(-3\) \(+\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}-2\beta _{2})q^{5}+\cdots\)
8019.2.a.b \(3\) \(64.032\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(3\) \(-3\) \(-\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
8019.2.a.c \(21\) \(64.032\) None \(-6\) \(0\) \(-12\) \(0\) \(-\) \(-\)
8019.2.a.d \(21\) \(64.032\) None \(0\) \(0\) \(-12\) \(0\) \(-\) \(-\)
8019.2.a.e \(21\) \(64.032\) None \(0\) \(0\) \(12\) \(0\) \(-\) \(+\)
8019.2.a.f \(21\) \(64.032\) None \(6\) \(0\) \(12\) \(0\) \(-\) \(+\)
8019.2.a.g \(36\) \(64.032\) None \(0\) \(0\) \(-9\) \(-9\) \(-\) \(-\)
8019.2.a.h \(36\) \(64.032\) None \(0\) \(0\) \(9\) \(-9\) \(+\) \(+\)
8019.2.a.i \(48\) \(64.032\) None \(-6\) \(0\) \(-24\) \(0\) \(+\) \(+\)
8019.2.a.j \(48\) \(64.032\) None \(6\) \(0\) \(24\) \(0\) \(+\) \(-\)
8019.2.a.k \(51\) \(64.032\) None \(0\) \(0\) \(-6\) \(12\) \(-\) \(+\)
8019.2.a.l \(51\) \(64.032\) None \(0\) \(0\) \(6\) \(12\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8019))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8019)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(729))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(891))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2673))\)\(^{\oplus 2}\)