Properties

Label 6028.2.a
Level 6028
Weight 2
Character orbit a
Rep. character \(\chi_{6028}(1,\cdot)\)
Character field \(\Q\)
Dimension 112
Newforms 6
Sturm bound 1656
Trace bound 5

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Defining parameters

Level: \( N \) = \( 6028 = 2^{2} \cdot 11 \cdot 137 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6028.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(1656\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6028))\).

Total New Old
Modular forms 834 112 722
Cusp forms 823 112 711
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.

\(2\)\(11\)\(137\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(27\)
\(-\)\(+\)\(-\)\(+\)\(29\)
\(-\)\(-\)\(+\)\(+\)\(25\)
\(-\)\(-\)\(-\)\(-\)\(31\)
Plus space\(+\)\(54\)
Minus space\(-\)\(58\)

Trace form

\(112q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 116q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(112q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 116q^{9} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 96q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut -\mathstrut 4q^{29} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 28q^{47} \) \(\mathstrut +\mathstrut 124q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 16q^{53} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 56q^{63} \) \(\mathstrut -\mathstrut 56q^{65} \) \(\mathstrut +\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut +\mathstrut 12q^{79} \) \(\mathstrut +\mathstrut 112q^{81} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 12q^{85} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 40q^{89} \) \(\mathstrut +\mathstrut 56q^{91} \) \(\mathstrut -\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6028))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 11 137
6028.2.a.a \(2\) \(48.134\) \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-5\) \(-7\) \(-\) \(-\) \(-\) \(q-\beta q^{3}+(-3+\beta )q^{5}+(-3-\beta )q^{7}+\cdots\)
6028.2.a.b \(2\) \(48.134\) \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(3\) \(5\) \(-\) \(+\) \(-\) \(q-\beta q^{3}+(1+\beta )q^{5}+(3-\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
6028.2.a.c \(25\) \(48.134\) None \(0\) \(-11\) \(-2\) \(-9\) \(-\) \(-\) \(+\)
6028.2.a.d \(27\) \(48.134\) None \(0\) \(-6\) \(1\) \(-14\) \(-\) \(+\) \(-\)
6028.2.a.e \(27\) \(48.134\) None \(0\) \(5\) \(-2\) \(7\) \(-\) \(+\) \(+\)
6028.2.a.f \(29\) \(48.134\) None \(0\) \(14\) \(9\) \(14\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(137))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(274))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(548))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1507))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3014))\)\(^{\oplus 2}\)