Properties

Label 8.14.a
Level $8$
Weight $14$
Character orbit 8.a
Rep. character $\chi_{8}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $14$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 8.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(8))\).

Total New Old
Modular forms 15 3 12
Cusp forms 11 3 8
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
\(+\)\(1\)
\(-\)\(2\)

Trace form

\( 3 q + 860 q^{3} + 14146 q^{5} - 29064 q^{7} + 1995319 q^{9} + O(q^{10}) \) \( 3 q + 860 q^{3} + 14146 q^{5} - 29064 q^{7} + 1995319 q^{9} + 9989716 q^{11} - 3843462 q^{13} + 84882920 q^{15} - 177525898 q^{17} + 206597196 q^{19} - 1370300832 q^{21} + 1639869544 q^{23} - 2551374099 q^{25} + 5792047640 q^{27} - 3556537878 q^{29} + 3514102752 q^{31} + 10657805840 q^{33} - 15413225904 q^{35} + 6628831266 q^{37} - 58427704504 q^{39} + 35734013598 q^{41} - 46788121548 q^{43} + 107010747322 q^{45} - 55058132016 q^{47} + 50399905803 q^{49} + 177530164600 q^{51} - 125287225454 q^{53} + 221032054584 q^{55} - 655927567760 q^{57} + 793560430372 q^{59} - 698520953142 q^{61} - 816280916328 q^{63} - 531488188292 q^{65} + 1645513736988 q^{67} + 1015234563872 q^{69} - 2427770841544 q^{71} + 3186234467454 q^{73} + 844579119460 q^{75} + 1067266262304 q^{77} - 6552713187408 q^{79} + 3041774504587 q^{81} + 3890337600524 q^{83} + 1613607983652 q^{85} - 15012516259320 q^{87} - 6046727859474 q^{89} + 19047242532624 q^{91} - 6946080702080 q^{93} - 9708727342456 q^{95} - 4437752016474 q^{97} + 42866396476420 q^{99} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(8))\) 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
8.14.a.a 8.a 1.a $1$ $8.578$ \(\Q\) None \(0\) \(-12\) \(-4330\) \(-139992\) $+$ $\mathrm{SU}(2)$ \(q-12q^{3}-4330q^{5}-139992q^{7}+\cdots\)
8.14.a.b 8.a 1.a $2$ $8.578$ \(\Q(\sqrt{781}) \) None \(0\) \(872\) \(18476\) \(110928\) $-$ $\mathrm{SU}(2)$ \(q+(436-\beta )q^{3}+(9238-12\beta )q^{5}+(55464+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(8)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)