Properties

Label 8046.2.a
Level 8046
Weight 2
Character orbit a
Rep. character \(\chi_{8046}(1,\cdot)\)
Character field \(\Q\)
Dimension 196
Newforms 20
Sturm bound 2700
Trace bound 5

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Defining parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)
Character field: \(\Q\)
Newforms: \( 20 \)
Sturm bound: \(2700\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8046))\).

Total New Old
Modular forms 1362 196 1166
Cusp forms 1339 196 1143
Eisenstein series 23 0 23

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

\(2\)\(3\)\(149\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(21\)
\(+\)\(+\)\(-\)\(-\)\(28\)
\(+\)\(-\)\(+\)\(-\)\(28\)
\(+\)\(-\)\(-\)\(+\)\(21\)
\(-\)\(+\)\(+\)\(-\)\(28\)
\(-\)\(+\)\(-\)\(+\)\(21\)
\(-\)\(-\)\(+\)\(+\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(28\)
Plus space\(+\)\(84\)
Minus space\(-\)\(112\)

Trace form

\(196q \) \(\mathstrut +\mathstrut 196q^{4} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(196q \) \(\mathstrut +\mathstrut 196q^{4} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 196q^{16} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 172q^{25} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 188q^{49} \) \(\mathstrut -\mathstrut 32q^{55} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut -\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 196q^{64} \) \(\mathstrut -\mathstrut 40q^{67} \) \(\mathstrut -\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut -\mathstrut 32q^{82} \) \(\mathstrut -\mathstrut 64q^{85} \) \(\mathstrut -\mathstrut 8q^{88} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8046))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 149
8046.2.a.a \(1\) \(64.248\) \(\Q\) None \(-1\) \(0\) \(2\) \(1\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
8046.2.a.b \(1\) \(64.248\) \(\Q\) None \(1\) \(0\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
8046.2.a.c \(2\) \(64.248\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+2\beta q^{5}+(1-2\beta )q^{7}-q^{8}+\cdots\)
8046.2.a.d \(2\) \(64.248\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+2\beta q^{5}+(1+2\beta )q^{7}+q^{8}+\cdots\)
8046.2.a.e \(8\) \(64.248\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(0\) \(-5\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(-1-\beta _{5})q^{7}+\cdots\)
8046.2.a.f \(8\) \(64.248\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(0\) \(-5\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-\beta _{1}q^{5}+(-1-\beta _{5})q^{7}+\cdots\)
8046.2.a.g \(9\) \(64.248\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(0\) \(4\) \(-4\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+(\beta _{1}-\beta _{5}+\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8046.2.a.h \(9\) \(64.248\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(0\) \(-4\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(-\beta _{1}+\beta _{5}-\beta _{7})q^{5}+\cdots\)
8046.2.a.i \(12\) \(64.248\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(0\) \(-5\) \(6\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-\beta _{1}q^{5}+(1-\beta _{5})q^{7}-q^{8}+\cdots\)
8046.2.a.j \(12\) \(64.248\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(0\) \(-3\) \(6\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{6})q^{7}-q^{8}+\cdots\)
8046.2.a.k \(12\) \(64.248\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(0\) \(3\) \(-6\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(-1-\beta _{9})q^{7}+\cdots\)
8046.2.a.l \(12\) \(64.248\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(0\) \(5\) \(-6\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}-q^{8}+\cdots\)
8046.2.a.m \(12\) \(64.248\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(-5\) \(-6\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots\)
8046.2.a.n \(12\) \(64.248\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(-3\) \(-6\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-\beta _{1}q^{5}+(-1-\beta _{9})q^{7}+\cdots\)
8046.2.a.o \(12\) \(64.248\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(3\) \(6\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+\beta _{1}q^{5}+(1+\beta _{6})q^{7}+q^{8}+\cdots\)
8046.2.a.p \(12\) \(64.248\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(5\) \(6\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+\beta _{1}q^{5}+(1-\beta _{5})q^{7}+q^{8}+\cdots\)
8046.2.a.q \(14\) \(64.248\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(0\) \(-2\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{11}q^{7}-q^{8}+\cdots\)
8046.2.a.r \(14\) \(64.248\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(14\) \(0\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{11}q^{7}+q^{8}+\cdots\)
8046.2.a.s \(16\) \(64.248\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(0\) \(-4\) \(6\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-\beta _{1}q^{5}+\beta _{7}q^{7}-q^{8}+\cdots\)
8046.2.a.t \(16\) \(64.248\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(0\) \(4\) \(6\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8046))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8046)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(149))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(298))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(447))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(894))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1341))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2682))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4023))\)\(^{\oplus 2}\)