Properties

Label 8.14.a
Level 8
Weight 14
Character orbit a
Rep. character \(\chi_{8}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(8))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
8.14.a.a \(1\) \(8.578\) \(\Q\) None \(0\) \(-12\) \(-4330\) \(-139992\) \(+\) \(q-12q^{3}-4330q^{5}-139992q^{7}+\cdots\)
8.14.a.b \(2\) \(8.578\) \(\Q(\sqrt{781}) \) None \(0\) \(872\) \(18476\) \(110928\) \(-\) \(q+(436-\beta )q^{3}+(9238-12\beta )q^{5}+(55464+\cdots)q^{7}+\cdots\)

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

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