Properties

Label 8.7.d
Level 8
Weight 7
Character orbit d
Rep. character \(\chi_{8}(3,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 2
Sturm bound 7
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 8.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(7\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(8, [\chi])\).

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

Trace form

\(5q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 20q^{4} \) \(\mathstrut +\mathstrut 28q^{6} \) \(\mathstrut -\mathstrut 264q^{8} \) \(\mathstrut +\mathstrut 727q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 20q^{4} \) \(\mathstrut +\mathstrut 28q^{6} \) \(\mathstrut -\mathstrut 264q^{8} \) \(\mathstrut +\mathstrut 727q^{9} \) \(\mathstrut -\mathstrut 1920q^{10} \) \(\mathstrut -\mathstrut 1362q^{11} \) \(\mathstrut +\mathstrut 4312q^{12} \) \(\mathstrut +\mathstrut 5760q^{14} \) \(\mathstrut -\mathstrut 10480q^{16} \) \(\mathstrut +\mathstrut 2442q^{17} \) \(\mathstrut -\mathstrut 21506q^{18} \) \(\mathstrut -\mathstrut 3938q^{19} \) \(\mathstrut +\mathstrut 31680q^{20} \) \(\mathstrut +\mathstrut 43132q^{22} \) \(\mathstrut -\mathstrut 61808q^{24} \) \(\mathstrut -\mathstrut 8275q^{25} \) \(\mathstrut -\mathstrut 59520q^{26} \) \(\mathstrut +\mathstrut 32860q^{27} \) \(\mathstrut +\mathstrut 59520q^{28} \) \(\mathstrut +\mathstrut 90240q^{30} \) \(\mathstrut -\mathstrut 81696q^{32} \) \(\mathstrut -\mathstrut 23500q^{33} \) \(\mathstrut -\mathstrut 68108q^{34} \) \(\mathstrut -\mathstrut 49920q^{35} \) \(\mathstrut +\mathstrut 75868q^{36} \) \(\mathstrut +\mathstrut 46428q^{38} \) \(\mathstrut -\mathstrut 13440q^{40} \) \(\mathstrut +\mathstrut 16698q^{41} \) \(\mathstrut +\mathstrut 38400q^{42} \) \(\mathstrut +\mathstrut 122542q^{43} \) \(\mathstrut -\mathstrut 112488q^{44} \) \(\mathstrut -\mathstrut 213120q^{46} \) \(\mathstrut +\mathstrut 326368q^{48} \) \(\mathstrut +\mathstrut 119765q^{49} \) \(\mathstrut +\mathstrut 232650q^{50} \) \(\mathstrut -\mathstrut 465412q^{51} \) \(\mathstrut -\mathstrut 254400q^{52} \) \(\mathstrut -\mathstrut 495368q^{54} \) \(\mathstrut +\mathstrut 349440q^{56} \) \(\mathstrut +\mathstrut 12500q^{57} \) \(\mathstrut +\mathstrut 516480q^{58} \) \(\mathstrut +\mathstrut 846990q^{59} \) \(\mathstrut -\mathstrut 716160q^{60} \) \(\mathstrut -\mathstrut 407040q^{62} \) \(\mathstrut +\mathstrut 726080q^{64} \) \(\mathstrut -\mathstrut 205440q^{65} \) \(\mathstrut +\mathstrut 717608q^{66} \) \(\mathstrut -\mathstrut 1386818q^{67} \) \(\mathstrut -\mathstrut 324312q^{68} \) \(\mathstrut -\mathstrut 360960q^{70} \) \(\mathstrut +\mathstrut 95656q^{72} \) \(\mathstrut -\mathstrut 149222q^{73} \) \(\mathstrut -\mathstrut 32640q^{74} \) \(\mathstrut +\mathstrut 2483950q^{75} \) \(\mathstrut -\mathstrut 88232q^{76} \) \(\mathstrut +\mathstrut 324480q^{78} \) \(\mathstrut -\mathstrut 1032960q^{80} \) \(\mathstrut -\mathstrut 186839q^{81} \) \(\mathstrut -\mathstrut 672428q^{82} \) \(\mathstrut -\mathstrut 2786082q^{83} \) \(\mathstrut +\mathstrut 602880q^{84} \) \(\mathstrut +\mathstrut 1588860q^{86} \) \(\mathstrut -\mathstrut 753392q^{88} \) \(\mathstrut +\mathstrut 403962q^{89} \) \(\mathstrut -\mathstrut 1296000q^{90} \) \(\mathstrut +\mathstrut 3398400q^{91} \) \(\mathstrut +\mathstrut 2743680q^{92} \) \(\mathstrut +\mathstrut 971520q^{94} \) \(\mathstrut -\mathstrut 1760192q^{96} \) \(\mathstrut +\mathstrut 895978q^{97} \) \(\mathstrut -\mathstrut 3332454q^{98} \) \(\mathstrut -\mathstrut 5702086q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(8, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
8.7.d.a \(1\) \(1.840\) \(\Q\) \(\Q(\sqrt{-2}) \) \(-8\) \(46\) \(0\) \(0\) \(q-8q^{2}+46q^{3}+2^{6}q^{4}-368q^{6}+\cdots\)
8.7.d.b \(4\) \(1.840\) 4.0.3803625.2 None \(2\) \(-48\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-13+2\beta _{1}+\beta _{2})q^{3}+(-12+\cdots)q^{4}+\cdots\)