Properties

Label 6016.2.a
Level 6016
Weight 2
Character orbit a
Rep. character \(\chi_{6016}(1,\cdot)\)
Character field \(\Q\)
Dimension 184
Newforms 20
Sturm bound 1536
Trace bound 13

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Defining parameters

Level: \( N \) = \( 6016 = 2^{7} \cdot 47 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6016.a (trivial)
Character field: \(\Q\)
Newforms: \( 20 \)
Sturm bound: \(1536\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6016))\).

Total New Old
Modular forms 784 184 600
Cusp forms 753 184 569
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.

\(2\)\(47\)FrickeDim.
\(+\)\(+\)\(+\)\(43\)
\(+\)\(-\)\(-\)\(51\)
\(-\)\(+\)\(-\)\(49\)
\(-\)\(-\)\(+\)\(41\)
Plus space\(+\)\(84\)
Minus space\(-\)\(100\)

Trace form

\(184q \) \(\mathstrut +\mathstrut 184q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(184q \) \(\mathstrut +\mathstrut 184q^{9} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 200q^{25} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 48q^{41} \) \(\mathstrut +\mathstrut 120q^{49} \) \(\mathstrut -\mathstrut 32q^{57} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut -\mathstrut 112q^{73} \) \(\mathstrut +\mathstrut 216q^{81} \) \(\mathstrut -\mathstrut 48q^{89} \) \(\mathstrut +\mathstrut 16q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6016))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 47
6016.2.a.a \(1\) \(48.038\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(-\) \(q-2q^{3}+q^{9}-4q^{13}+2q^{17}+8q^{19}+\cdots\)
6016.2.a.b \(1\) \(48.038\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(q-2q^{3}+q^{9}+4q^{13}+2q^{17}+8q^{19}+\cdots\)
6016.2.a.c \(1\) \(48.038\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(+\) \(+\) \(q+2q^{3}+q^{9}-4q^{13}+2q^{17}-8q^{19}+\cdots\)
6016.2.a.d \(1\) \(48.038\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(q+2q^{3}+q^{9}+4q^{13}+2q^{17}-8q^{19}+\cdots\)
6016.2.a.e \(8\) \(48.038\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-2\) \(-4\) \(6\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(1+\beta _{6})q^{7}+\cdots\)
6016.2.a.f \(8\) \(48.038\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-2\) \(4\) \(-6\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(-1-\beta _{6})q^{7}+\cdots\)
6016.2.a.g \(8\) \(48.038\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(2\) \(-4\) \(-6\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
6016.2.a.h \(8\) \(48.038\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(2\) \(4\) \(6\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(1+\beta _{6})q^{7}+\cdots\)
6016.2.a.i \(10\) \(48.038\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-2\) \(-4\) \(2\) \(-\) \(-\) \(q-\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)
6016.2.a.j \(10\) \(48.038\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-2\) \(4\) \(-2\) \(+\) \(+\) \(q-\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)
6016.2.a.k \(10\) \(48.038\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(2\) \(-4\) \(-2\) \(+\) \(+\) \(q+\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)
6016.2.a.l \(10\) \(48.038\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(2\) \(4\) \(2\) \(+\) \(-\) \(q+\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)
6016.2.a.m \(13\) \(48.038\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-4\) \(-6\) \(2\) \(-\) \(-\) \(q-\beta _{1}q^{3}-\beta _{8}q^{5}+\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.n \(13\) \(48.038\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-4\) \(6\) \(-2\) \(-\) \(+\) \(q-\beta _{1}q^{3}+\beta _{8}q^{5}-\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.o \(13\) \(48.038\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(4\) \(-6\) \(-2\) \(-\) \(+\) \(q+\beta _{1}q^{3}-\beta _{8}q^{5}-\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.p \(13\) \(48.038\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(4\) \(6\) \(2\) \(+\) \(-\) \(q+\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.q \(14\) \(48.038\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-2\) \(-6\) \(-2\) \(+\) \(+\) \(q-\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.r \(14\) \(48.038\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-2\) \(6\) \(2\) \(+\) \(-\) \(q-\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.s \(14\) \(48.038\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(2\) \(-6\) \(2\) \(+\) \(-\) \(q+\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.t \(14\) \(48.038\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(2\) \(6\) \(-2\) \(-\) \(+\) \(q+\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(94))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(188))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(376))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(752))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1504))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3008))\)\(^{\oplus 2}\)