Properties

Label 6004.2.a
Level 6004
Weight 2
Character orbit a
Rep. character \(\chi_{6004}(1,\cdot)\)
Character field \(\Q\)
Dimension 118
Newforms 8
Sturm bound 1600
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)
Character field: \(\Q\)
Newforms: \( 8 \)
Sturm bound: \(1600\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6004))\).

Total New Old
Modular forms 806 118 688
Cusp forms 795 118 677
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.

\(2\)\(19\)\(79\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(32\)
\(-\)\(+\)\(-\)\(+\)\(26\)
\(-\)\(-\)\(+\)\(+\)\(27\)
\(-\)\(-\)\(-\)\(-\)\(33\)
Plus space\(+\)\(53\)
Minus space\(-\)\(65\)

Trace form

\(118q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 126q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(118q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 126q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 120q^{25} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 12q^{29} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 44q^{33} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 6q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 14q^{47} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut +\mathstrut 20q^{51} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 30q^{61} \) \(\mathstrut +\mathstrut 2q^{63} \) \(\mathstrut +\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 134q^{81} \) \(\mathstrut +\mathstrut 26q^{85} \) \(\mathstrut +\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 28q^{93} \) \(\mathstrut -\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 14q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6004))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19 79
6004.2.a.a \(1\) \(47.942\) \(\Q\) None \(0\) \(-2\) \(-1\) \(-5\) \(-\) \(+\) \(-\) \(q-2q^{3}-q^{5}-5q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
6004.2.a.b \(1\) \(47.942\) \(\Q\) None \(0\) \(0\) \(1\) \(-4\) \(-\) \(+\) \(+\) \(q+q^{5}-4q^{7}-3q^{9}+2q^{11}-4q^{13}+\cdots\)
6004.2.a.c \(1\) \(47.942\) \(\Q\) None \(0\) \(1\) \(-3\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{3}-3q^{5}-q^{7}-2q^{9}+5q^{13}+\cdots\)
6004.2.a.d \(8\) \(47.942\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(4\) \(1\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{5}-\beta _{4}q^{7}-3q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
6004.2.a.e \(24\) \(47.942\) None \(0\) \(1\) \(9\) \(2\) \(-\) \(-\) \(-\)
6004.2.a.f \(25\) \(47.942\) None \(0\) \(4\) \(-8\) \(2\) \(-\) \(+\) \(-\)
6004.2.a.g \(27\) \(47.942\) None \(0\) \(-4\) \(-10\) \(-8\) \(-\) \(-\) \(+\)
6004.2.a.h \(31\) \(47.942\) None \(0\) \(-4\) \(10\) \(11\) \(-\) \(+\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(79))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(158))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(316))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1501))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3002))\)\(^{\oplus 2}\)