Properties

Label 6024.2.a
Level 6024
Weight 2
Character orbit a
Rep. character \(\chi_{6024}(1,\cdot)\)
Character field \(\Q\)
Dimension 124
Newforms 18
Sturm bound 2016
Trace bound 7

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 6024 = 2^{3} \cdot 3 \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6024.a (trivial)
Character field: \(\Q\)
Newforms: \( 18 \)
Sturm bound: \(2016\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6024))\).

Total New Old
Modular forms 1016 124 892
Cusp forms 1001 124 877
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.

\(2\)\(3\)\(251\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(15\)
\(+\)\(+\)\(-\)\(-\)\(16\)
\(+\)\(-\)\(+\)\(-\)\(20\)
\(+\)\(-\)\(-\)\(+\)\(12\)
\(-\)\(+\)\(+\)\(-\)\(14\)
\(-\)\(+\)\(-\)\(+\)\(16\)
\(-\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(18\)
Plus space\(+\)\(56\)
Minus space\(-\)\(68\)

Trace form

\(124q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 124q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(124q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 124q^{9} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 116q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 112q^{49} \) \(\mathstrut +\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 24q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 16q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 28q^{79} \) \(\mathstrut +\mathstrut 124q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut -\mathstrut 12q^{89} \) \(\mathstrut +\mathstrut 40q^{91} \) \(\mathstrut +\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 16q^{95} \) \(\mathstrut +\mathstrut 24q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6024))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 251
6024.2.a.a \(1\) \(48.102\) \(\Q\) None \(0\) \(-1\) \(-3\) \(1\) \(-\) \(+\) \(+\) \(q-q^{3}-3q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6024.2.a.b \(1\) \(48.102\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-3q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6024.2.a.c \(1\) \(48.102\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}+2q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
6024.2.a.d \(1\) \(48.102\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6024.2.a.e \(1\) \(48.102\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
6024.2.a.f \(1\) \(48.102\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(+\) \(-\) \(-\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
6024.2.a.g \(1\) \(48.102\) \(\Q\) None \(0\) \(1\) \(1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
6024.2.a.h \(2\) \(48.102\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
6024.2.a.i \(2\) \(48.102\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(-6\) \(-\) \(+\) \(-\) \(q-q^{3}+(1+\beta )q^{5}-3q^{7}+q^{9}+2q^{11}+\cdots\)
6024.2.a.j \(3\) \(48.102\) 3.3.148.1 None \(0\) \(3\) \(1\) \(-9\) \(+\) \(-\) \(-\) \(q+q^{3}+\beta _{2}q^{5}-3q^{7}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
6024.2.a.k \(8\) \(48.102\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(-5\) \(1\) \(+\) \(-\) \(-\) \(q+q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-\beta _{3}-\beta _{7})q^{7}+\cdots\)
6024.2.a.l \(11\) \(48.102\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(-11\) \(6\) \(-5\) \(-\) \(+\) \(+\) \(q-q^{3}+(1+\beta _{3})q^{5}+(\beta _{3}-\beta _{10})q^{7}+\cdots\)
6024.2.a.m \(11\) \(48.102\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(11\) \(-3\) \(-10\) \(-\) \(-\) \(+\) \(q+q^{3}+\beta _{5}q^{5}+(-1-\beta _{10})q^{7}+q^{9}+\cdots\)
6024.2.a.n \(14\) \(48.102\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-14\) \(-7\) \(1\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1+\beta _{1})q^{5}-\beta _{3}q^{7}+q^{9}+\cdots\)
6024.2.a.o \(14\) \(48.102\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-14\) \(-3\) \(7\) \(-\) \(+\) \(-\) \(q-q^{3}-\beta _{1}q^{5}+(1-\beta _{7})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
6024.2.a.p \(14\) \(48.102\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-14\) \(6\) \(3\) \(+\) \(+\) \(-\) \(q-q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+q^{9}-\beta _{8}q^{11}+\cdots\)
6024.2.a.q \(18\) \(48.102\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(18\) \(1\) \(7\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta _{1}q^{5}-\beta _{14}q^{7}+q^{9}-\beta _{15}q^{11}+\cdots\)
6024.2.a.r \(20\) \(48.102\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(20\) \(9\) \(9\) \(+\) \(-\) \(+\) \(q+q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{9}-\beta _{13}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6024))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(753))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1004))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1506))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3012))\)\(^{\oplus 2}\)