Properties

Label 6032.2.a
Level 6032
Weight 2
Character orbit a
Rep. character \(\chi_{6032}(1,\cdot)\)
Character field \(\Q\)
Dimension 168
Newforms 31
Sturm bound 1680
Trace bound 5

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Defining parameters

Level: \( N \) = \( 6032 = 2^{4} \cdot 13 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6032.a (trivial)
Character field: \(\Q\)
Newforms: \( 31 \)
Sturm bound: \(1680\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6032))\).

Total New Old
Modular forms 852 168 684
Cusp forms 829 168 661
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.

\(2\)\(13\)\(29\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(19\)
\(+\)\(+\)\(-\)\(-\)\(23\)
\(+\)\(-\)\(+\)\(-\)\(23\)
\(+\)\(-\)\(-\)\(+\)\(19\)
\(-\)\(+\)\(+\)\(-\)\(23\)
\(-\)\(+\)\(-\)\(+\)\(19\)
\(-\)\(-\)\(+\)\(+\)\(19\)
\(-\)\(-\)\(-\)\(-\)\(23\)
Plus space\(+\)\(76\)
Minus space\(-\)\(92\)

Trace form

\(168q \) \(\mathstrut +\mathstrut 176q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(168q \) \(\mathstrut +\mathstrut 176q^{9} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 168q^{25} \) \(\mathstrut -\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 28q^{31} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut +\mathstrut 168q^{49} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut +\mathstrut 40q^{63} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 184q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut +\mathstrut 8q^{89} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 24q^{97} \) \(\mathstrut -\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6032))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 13 29
6032.2.a.a \(1\) \(48.166\) \(\Q\) None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(-\) \(-\) \(q-2q^{3}-2q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
6032.2.a.b \(1\) \(48.166\) \(\Q\) None \(0\) \(-1\) \(-3\) \(3\) \(-\) \(+\) \(-\) \(q-q^{3}-3q^{5}+3q^{7}-2q^{9}+4q^{11}+\cdots\)
6032.2.a.c \(1\) \(48.166\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}-2q^{9}+6q^{11}+q^{13}+\cdots\)
6032.2.a.d \(1\) \(48.166\) \(\Q\) None \(0\) \(-1\) \(3\) \(1\) \(-\) \(-\) \(+\) \(q-q^{3}+3q^{5}+q^{7}-2q^{9}+q^{13}-3q^{15}+\cdots\)
6032.2.a.e \(1\) \(48.166\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{5}-3q^{9}+4q^{11}+q^{13}+2q^{17}+\cdots\)
6032.2.a.f \(1\) \(48.166\) \(\Q\) None \(0\) \(0\) \(2\) \(-4\) \(+\) \(-\) \(+\) \(q+2q^{5}-4q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots\)
6032.2.a.g \(1\) \(48.166\) \(\Q\) None \(0\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(-\) \(q+2q^{3}-2q^{5}-2q^{7}+q^{9}+q^{13}+\cdots\)
6032.2.a.h \(1\) \(48.166\) \(\Q\) None \(0\) \(3\) \(-1\) \(5\) \(+\) \(-\) \(+\) \(q+3q^{3}-q^{5}+5q^{7}+6q^{9}-4q^{11}+\cdots\)
6032.2.a.i \(2\) \(48.166\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(-6\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{3}+2\beta q^{5}+(-3+\beta )q^{7}+\cdots\)
6032.2.a.j \(2\) \(48.166\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(1\) \(-3\) \(-\) \(-\) \(+\) \(q-2\beta q^{3}+(1-\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
6032.2.a.k \(2\) \(48.166\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-4\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}+(-2-\beta )q^{5}+(-1-2\beta )q^{7}+\cdots\)
6032.2.a.l \(4\) \(48.166\) 4.4.7232.1 None \(0\) \(-2\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(q+(-\beta _{1}+\beta _{3})q^{3}+(-\beta _{1}+2\beta _{3})q^{5}+\cdots\)
6032.2.a.m \(4\) \(48.166\) 4.4.27004.1 None \(0\) \(0\) \(7\) \(-3\) \(-\) \(+\) \(-\) \(q+(\beta _{1}+\beta _{3})q^{3}+(2-\beta _{1})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
6032.2.a.n \(5\) \(48.166\) 5.5.1220776.1 None \(0\) \(-3\) \(6\) \(2\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
6032.2.a.o \(5\) \(48.166\) 5.5.161121.1 None \(0\) \(2\) \(-6\) \(5\) \(-\) \(-\) \(+\) \(q+\beta _{4}q^{3}+(-1-\beta _{1})q^{5}+(1+\beta _{3})q^{7}+\cdots\)
6032.2.a.p \(5\) \(48.166\) 5.5.149169.1 None \(0\) \(2\) \(-2\) \(-3\) \(-\) \(+\) \(-\) \(q+\beta _{4}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
6032.2.a.q \(5\) \(48.166\) 5.5.36497.1 None \(0\) \(4\) \(-2\) \(11\) \(-\) \(+\) \(+\) \(q+(1+\beta _{4})q^{3}+(-2\beta _{1}+\beta _{3}-\beta _{4})q^{5}+\cdots\)
6032.2.a.r \(5\) \(48.166\) 5.5.202817.1 None \(0\) \(4\) \(2\) \(15\) \(-\) \(-\) \(-\) \(q+(1+\beta _{3})q^{3}+(1+\beta _{3}-\beta _{4})q^{5}+(3+\cdots)q^{7}+\cdots\)
6032.2.a.s \(6\) \(48.166\) 6.6.226964648.1 None \(0\) \(-2\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q-\beta _{4}q^{3}+(1+\beta _{3})q^{5}+\beta _{1}q^{7}+(1-\beta _{5})q^{9}+\cdots\)
6032.2.a.t \(6\) \(48.166\) 6.6.11341289.1 None \(0\) \(3\) \(-5\) \(2\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
6032.2.a.u \(7\) \(48.166\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-2\) \(-2\) \(-7\) \(-\) \(+\) \(-\) \(q-\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
6032.2.a.v \(9\) \(48.166\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-2\) \(-4\) \(3\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{3}q^{7}+(\beta _{3}-\beta _{7}+\cdots)q^{9}+\cdots\)
6032.2.a.w \(9\) \(48.166\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-2\) \(-2\) \(1\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6032.2.a.x \(9\) \(48.166\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-2\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{4})q^{7}+\cdots\)
6032.2.a.y \(9\) \(48.166\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(2\) \(-17\) \(-\) \(-\) \(+\) \(q+\beta _{8}q^{3}+\beta _{3}q^{5}+(-2+\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots\)
6032.2.a.z \(10\) \(48.166\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-3\) \(4\) \(3\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{6}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
6032.2.a.ba \(10\) \(48.166\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-2\) \(5\) \(2\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{3}-\beta _{9}q^{5}-\beta _{2}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
6032.2.a.bb \(10\) \(48.166\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(3\) \(-5\) \(0\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{3}-\beta _{7}q^{5}-\beta _{4}q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
6032.2.a.bc \(11\) \(48.166\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(6\) \(-2\) \(3\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
6032.2.a.bd \(12\) \(48.166\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-6\) \(3\) \(-6\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{3}+\beta _{6}q^{5}+(-1-\beta _{5}+\cdots)q^{7}+\cdots\)
6032.2.a.be \(13\) \(48.166\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(4\) \(5\) \(-6\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}-\beta _{7}q^{5}-\beta _{5}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6032))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6032)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(377))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(754))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1508))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3016))\)\(^{\oplus 2}\)