Properties

Label 8.10.a
Level $8$
Weight $10$
Character orbit 8.a
Rep. character $\chi_{8}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $10$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 8.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(8))\).

Total New Old
Modular forms 11 2 9
Cusp forms 7 2 5
Eisenstein series 4 0 4

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

\(2\)Dim
\(+\)\(1\)
\(-\)\(1\)

Trace form

\( 2 q + 8 q^{3} - 564 q^{5} + 5904 q^{7} - 31142 q^{9} + O(q^{10}) \) \( 2 q + 8 q^{3} - 564 q^{5} + 5904 q^{7} - 31142 q^{9} + 97560 q^{11} - 188836 q^{13} + 227120 q^{15} - 171228 q^{17} - 53720 q^{19} + 957504 q^{21} - 2602704 q^{23} + 2675326 q^{25} - 216496 q^{27} + 1154940 q^{29} - 5041088 q^{31} - 5352352 q^{33} + 24483936 q^{35} - 13132788 q^{37} - 11273872 q^{39} - 15066924 q^{41} + 45379928 q^{43} + 10617052 q^{45} - 79274400 q^{47} + 43184626 q^{49} + 29265040 q^{51} + 39751980 q^{53} - 188304496 q^{55} + 67197088 q^{57} + 173485944 q^{59} - 12522052 q^{61} - 84460080 q^{63} - 241267032 q^{65} + 195391624 q^{67} - 85728064 q^{69} + 335441808 q^{71} - 7997164 q^{73} - 118666760 q^{75} - 366658368 q^{77} - 34286944 q^{79} + 323563378 q^{81} - 291672408 q^{83} + 886884952 q^{85} - 187171344 q^{87} - 6641100 q^{89} - 1756556064 q^{91} + 479023360 q^{93} + 1902684144 q^{95} + 204662980 q^{97} - 1565047496 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(8))\) 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
8.10.a.a 8.a 1.a $1$ $4.120$ \(\Q\) None \(0\) \(-60\) \(-2074\) \(-4344\) $+$ $\mathrm{SU}(2)$ \(q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots\)
8.10.a.b 8.a 1.a $1$ $4.120$ \(\Q\) None \(0\) \(68\) \(1510\) \(10248\) $-$ $\mathrm{SU}(2)$ \(q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(8)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)