Properties

Label 6008.2.a
Level 6008
Weight 2
Character orbit a
Rep. character \(\chi_{6008}(1,\cdot)\)
Character field \(\Q\)
Dimension 188
Newforms 5
Sturm bound 1504
Trace bound 3

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Defining parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(1504\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6008))\).

Total New Old
Modular forms 756 188 568
Cusp forms 749 188 561
Eisenstein series 7 0 7

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

\(2\)\(751\)FrickeDim.
\(+\)\(+\)\(+\)\(44\)
\(+\)\(-\)\(-\)\(50\)
\(-\)\(+\)\(-\)\(50\)
\(-\)\(-\)\(+\)\(44\)
Plus space\(+\)\(88\)
Minus space\(-\)\(100\)

Trace form

\(188q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 188q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(188q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 188q^{9} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 200q^{25} \) \(\mathstrut +\mathstrut 20q^{27} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 204q^{49} \) \(\mathstrut +\mathstrut 24q^{51} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 28q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 26q^{75} \) \(\mathstrut -\mathstrut 12q^{79} \) \(\mathstrut +\mathstrut 204q^{81} \) \(\mathstrut +\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 20q^{93} \) \(\mathstrut +\mathstrut 8q^{95} \) \(\mathstrut +\mathstrut 28q^{97} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6008))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 751
6008.2.a.a \(1\) \(47.974\) \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) \(+\) \(-\) \(q-2q^{5}-4q^{7}-3q^{9}-q^{13}-6q^{17}+\cdots\)
6008.2.a.b \(44\) \(47.974\) None \(0\) \(-14\) \(7\) \(-20\) \(+\) \(+\)
6008.2.a.c \(44\) \(47.974\) None \(0\) \(-4\) \(-21\) \(-10\) \(-\) \(-\)
6008.2.a.d \(49\) \(47.974\) None \(0\) \(14\) \(-7\) \(22\) \(+\) \(-\)
6008.2.a.e \(50\) \(47.974\) None \(0\) \(6\) \(23\) \(12\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6008))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(751))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1502))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3004))\)\(^{\oplus 2}\)