Properties

Label 2.8.a
Level $2$
Weight $8$
Character orbit 2.a
Rep. character $\chi_{2}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 2.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(2))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

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.
\(+\)\(1\)

Trace form

\( q - 8 q^{2} + 12 q^{3} + 64 q^{4} - 210 q^{5} - 96 q^{6} + 1016 q^{7} - 512 q^{8} - 2043 q^{9} + O(q^{10}) \) \( q - 8 q^{2} + 12 q^{3} + 64 q^{4} - 210 q^{5} - 96 q^{6} + 1016 q^{7} - 512 q^{8} - 2043 q^{9} + 1680 q^{10} + 1092 q^{11} + 768 q^{12} + 1382 q^{13} - 8128 q^{14} - 2520 q^{15} + 4096 q^{16} + 14706 q^{17} + 16344 q^{18} - 39940 q^{19} - 13440 q^{20} + 12192 q^{21} - 8736 q^{22} + 68712 q^{23} - 6144 q^{24} - 34025 q^{25} - 11056 q^{26} - 50760 q^{27} + 65024 q^{28} - 102570 q^{29} + 20160 q^{30} + 227552 q^{31} - 32768 q^{32} + 13104 q^{33} - 117648 q^{34} - 213360 q^{35} - 130752 q^{36} + 160526 q^{37} + 319520 q^{38} + 16584 q^{39} + 107520 q^{40} + 10842 q^{41} - 97536 q^{42} - 630748 q^{43} + 69888 q^{44} + 429030 q^{45} - 549696 q^{46} + 472656 q^{47} + 49152 q^{48} + 208713 q^{49} + 272200 q^{50} + 176472 q^{51} + 88448 q^{52} - 1494018 q^{53} + 406080 q^{54} - 229320 q^{55} - 520192 q^{56} - 479280 q^{57} + 820560 q^{58} + 2640660 q^{59} - 161280 q^{60} + 827702 q^{61} - 1820416 q^{62} - 2075688 q^{63} + 262144 q^{64} - 290220 q^{65} - 104832 q^{66} - 126004 q^{67} + 941184 q^{68} + 824544 q^{69} + 1706880 q^{70} - 1414728 q^{71} + 1046016 q^{72} + 980282 q^{73} - 1284208 q^{74} - 408300 q^{75} - 2556160 q^{76} + 1109472 q^{77} - 132672 q^{78} - 3566800 q^{79} - 860160 q^{80} + 3858921 q^{81} - 86736 q^{82} + 5672892 q^{83} + 780288 q^{84} - 3088260 q^{85} + 5045984 q^{86} - 1230840 q^{87} - 559104 q^{88} - 11951190 q^{89} - 3432240 q^{90} + 1404112 q^{91} + 4397568 q^{92} + 2730624 q^{93} - 3781248 q^{94} + 8387400 q^{95} - 393216 q^{96} + 8682146 q^{97} - 1669704 q^{98} - 2230956 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.8.a.a \(1\) \(0.625\) \(\Q\) None \(-8\) \(12\) \(-210\) \(1016\) \(+\) \(q-8q^{2}+12q^{3}+2^{6}q^{4}-210q^{5}+\cdots\)