Properties

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

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Defining parameters

Level: \( N \) \(=\) \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6039.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6039))\) into newform subspaces

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

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