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Properties

Label 8.18.a
Level $8$
Weight $18$
Character orbit 8.a
Rep. character $\chi_{8}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $18$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 8.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(8))\).

Total New Old
Modular forms 19 4 15
Cusp forms 15 4 11
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
\(+\)\(2\)
\(-\)\(2\)

Trace form

\( 4 q + 10640 q^{3} - 845544 q^{5} - 19265760 q^{7} + 134939956 q^{9} + O(q^{10}) \) \( 4 q + 10640 q^{3} - 845544 q^{5} - 19265760 q^{7} + 134939956 q^{9} - 39796560 q^{11} + 163998520 q^{13} - 8263058080 q^{15} + 12228814920 q^{17} + 96146659280 q^{19} - 313163478912 q^{21} + 221659563360 q^{23} - 325010017924 q^{25} + 2500686288800 q^{27} - 5251084703880 q^{29} + 8873782434944 q^{31} - 27075363085120 q^{33} + 56561374769856 q^{35} - 71506917316200 q^{37} + 92051021828576 q^{39} - 115990332949848 q^{41} + 136636971765040 q^{43} - 299350264536008 q^{45} + 302317000923840 q^{47} + 275068780803812 q^{49} - 354576680645600 q^{51} - 100542682473000 q^{53} - 875924195258336 q^{55} + 1646216068705600 q^{57} - 1728362237211792 q^{59} + 4829676956350456 q^{61} - 6870031547284320 q^{63} + 5455158737805648 q^{65} - 4674219417808240 q^{67} + 806157717690752 q^{69} + 2027324105089056 q^{71} - 5910999148949720 q^{73} + 16715682746477680 q^{75} - 11271437651625600 q^{77} + 12459538601703232 q^{79} - 36731319913087004 q^{81} + 35426115577045200 q^{83} - 38070216039124048 q^{85} + 49145287201594080 q^{87} - 67927937696017560 q^{89} + 90023701626551232 q^{91} + 29927544138703360 q^{93} - 81522827988999456 q^{95} - 16108478251471480 q^{97} - 37182223131302672 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(8))\) 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
8.18.a.a 8.a 1.a $2$ $14.658$ \(\Q(\sqrt{2146}) \) None \(0\) \(-952\) \(-53620\) \(-333168\) $-$ $\mathrm{SU}(2)$ \(q+(-476+\beta )q^{3}+(-26810+60\beta )q^{5}+\cdots\)
8.18.a.b 8.a 1.a $2$ $14.658$ \(\Q(\sqrt{114}) \) None \(0\) \(11592\) \(-791924\) \(-18932592\) $+$ $\mathrm{SU}(2)$ \(q+(5796+\beta )q^{3}+(-395962-68\beta )q^{5}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(8)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)