↑

Properties

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

Related objects

Downloads

Learn more

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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8.7.d.a 8.d 8.d $1$ $1.840$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-8\) \(46\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-8q^{2}+46q^{3}+2^{6}q^{4}-368q^{6}+\cdots\)
8.7.d.b 8.d 8.d $4$ $1.840$ 4.0.3803625.2 None \(2\) \(-48\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-13+2\beta _{1}+\beta _{2})q^{3}+(-12+\cdots)q^{4}+\cdots\)