Properties

Label 6039.2.a
Level 6039
Weight 2
Character orbit a
Rep. character \(\chi_{6039}(1,\cdot)\)
Character field \(\Q\)
Dimension 250
Newforms 16
Sturm bound 1488
Trace bound 7

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6039.a (trivial)
Character field: \(\Q\)
Newforms: \( 16 \)
Sturm bound: \(1488\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6039))\).

Total New Old
Modular forms 752 250 502
Cusp forms 737 250 487
Eisenstein series 15 0 15

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

\(3\)\(11\)\(61\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(25\)
\(+\)\(+\)\(-\)\(-\)\(25\)
\(+\)\(-\)\(+\)\(-\)\(25\)
\(+\)\(-\)\(-\)\(+\)\(25\)
\(-\)\(+\)\(+\)\(-\)\(44\)
\(-\)\(+\)\(-\)\(+\)\(29\)
\(-\)\(-\)\(+\)\(+\)\(31\)
\(-\)\(-\)\(-\)\(-\)\(46\)
Plus space\(+\)\(110\)
Minus space\(-\)\(140\)

Trace form

\(250q \) \(\mathstrut +\mathstrut 250q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(250q \) \(\mathstrut +\mathstrut 250q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 20q^{14} \) \(\mathstrut +\mathstrut 242q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 236q^{25} \) \(\mathstrut +\mathstrut 16q^{26} \) \(\mathstrut +\mathstrut 20q^{28} \) \(\mathstrut -\mathstrut 20q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut +\mathstrut 32q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 40q^{38} \) \(\mathstrut +\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut +\mathstrut 32q^{46} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 250q^{49} \) \(\mathstrut +\mathstrut 40q^{50} \) \(\mathstrut +\mathstrut 4q^{52} \) \(\mathstrut +\mathstrut 16q^{53} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 56q^{56} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut +\mathstrut 38q^{59} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 186q^{64} \) \(\mathstrut +\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 30q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut +\mathstrut 84q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 28q^{73} \) \(\mathstrut +\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 88q^{76} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 68q^{80} \) \(\mathstrut +\mathstrut 8q^{82} \) \(\mathstrut +\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 20q^{86} \) \(\mathstrut +\mathstrut 26q^{89} \) \(\mathstrut -\mathstrut 64q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut 26q^{97} \) \(\mathstrut +\mathstrut 136q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6039))\) 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 61
6039.2.a.a \(5\) \(48.222\) 5.5.24217.1 None \(2\) \(0\) \(2\) \(-1\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2}+\beta _{4})q^{4}+\beta _{2}q^{5}+\cdots\)
6039.2.a.b \(6\) \(48.222\) 6.6.2661761.1 None \(0\) \(0\) \(1\) \(-5\) \(-\) \(-\) \(+\) \(q-\beta _{3}q^{2}-\beta _{5}q^{4}+(-\beta _{1}+\beta _{3}-\beta _{5})q^{5}+\cdots\)
6039.2.a.c \(11\) \(48.222\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(2\) \(0\) \(1\) \(-11\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
6039.2.a.d \(11\) \(48.222\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(4\) \(0\) \(13\) \(-5\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{5}+\beta _{6})q^{4}+(1-\beta _{10})q^{5}+\cdots\)
6039.2.a.e \(12\) \(48.222\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(0\) \(3\) \(-9\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
6039.2.a.f \(12\) \(48.222\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(7\) \(0\) \(7\) \(-15\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
6039.2.a.g \(13\) \(48.222\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-4\) \(0\) \(-7\) \(5\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots\)
6039.2.a.h \(13\) \(48.222\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-4\) \(0\) \(-7\) \(7\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{5})q^{5}+\cdots\)
6039.2.a.i \(13\) \(48.222\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-2\) \(0\) \(-3\) \(11\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+(1+\beta _{11}+\cdots)q^{7}+\cdots\)
6039.2.a.j \(14\) \(48.222\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(1\) \(0\) \(-1\) \(9\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+(1+\cdots)q^{7}+\cdots\)
6039.2.a.k \(19\) \(48.222\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(-5\) \(0\) \(0\) \(9\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}-\beta _{16}q^{7}+\cdots\)
6039.2.a.l \(21\) \(48.222\) None \(0\) \(0\) \(-7\) \(5\) \(-\) \(-\) \(-\)
6039.2.a.m \(25\) \(48.222\) None \(-5\) \(0\) \(-12\) \(-4\) \(+\) \(-\) \(-\)
6039.2.a.n \(25\) \(48.222\) None \(-5\) \(0\) \(-4\) \(4\) \(+\) \(+\) \(+\)
6039.2.a.o \(25\) \(48.222\) None \(5\) \(0\) \(4\) \(4\) \(+\) \(-\) \(+\)
6039.2.a.p \(25\) \(48.222\) None \(5\) \(0\) \(12\) \(-4\) \(+\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6039))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6039)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(549))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(671))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2013))\)\(^{\oplus 2}\)