Properties

Label 6008.2.a
Level $6008$
Weight $2$
Character orbit 6008.a
Rep. character $\chi_{6008}(1,\cdot)$
Character field $\Q$
Dimension $188$
Newform subspaces $5$
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: \(\Q\)
Newform subspaces: \( 5 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6008))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 751
6008.2.a.a 6008.a 1.a $1$ $47.974$ \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}-3q^{9}-q^{13}-6q^{17}+\cdots\)
6008.2.a.b 6008.a 1.a $44$ $47.974$ None \(0\) \(-14\) \(7\) \(-20\) $+$ $+$ $\mathrm{SU}(2)$
6008.2.a.c 6008.a 1.a $44$ $47.974$ None \(0\) \(-4\) \(-21\) \(-10\) $-$ $-$ $\mathrm{SU}(2)$
6008.2.a.d 6008.a 1.a $49$ $47.974$ None \(0\) \(14\) \(-7\) \(22\) $+$ $-$ $\mathrm{SU}(2)$
6008.2.a.e 6008.a 1.a $50$ $47.974$ None \(0\) \(6\) \(23\) \(12\) $-$ $+$ $\mathrm{SU}(2)$

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

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