↑

Properties

Label 8.11.d
Level $8$
Weight $11$
Character orbit 8.d
Rep. character $\chi_{8}(3,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $2$
Sturm bound $11$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 11 \)
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: \(11\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(8, [\chi])\).

Total New Old
Modular forms 11 11 0
Cusp forms 9 9 0
Eisenstein series 2 2 0

Trace form

\( 9 q + 10 q^{2} - 2 q^{3} + 1236 q^{4} + 10012 q^{6} - 32840 q^{8} + 137779 q^{9} + O(q^{10}) \) \( 9 q + 10 q^{2} - 2 q^{3} + 1236 q^{4} + 10012 q^{6} - 32840 q^{8} + 137779 q^{9} + 9120 q^{10} + 45902 q^{11} - 313448 q^{12} - 400320 q^{14} - 938736 q^{16} + 452882 q^{17} - 2477042 q^{18} + 5107038 q^{19} + 2557440 q^{20} + 4666812 q^{22} - 4000112 q^{24} - 9027135 q^{25} + 1891680 q^{26} - 26107748 q^{27} + 18286080 q^{28} + 67026240 q^{30} - 97571360 q^{32} - 27349372 q^{33} - 142063212 q^{34} + 53736960 q^{35} + 228065116 q^{36} + 267808988 q^{38} - 357584640 q^{40} + 54890402 q^{41} - 576155520 q^{42} + 204294990 q^{43} + 628067288 q^{44} + 851947200 q^{46} - 1648174112 q^{48} + 202043001 q^{49} - 1981861190 q^{50} - 673729540 q^{51} + 2420759040 q^{52} + 3511590520 q^{54} - 2928529920 q^{56} - 215783068 q^{57} - 3245264160 q^{58} - 44598418 q^{59} + 5250055680 q^{60} + 4060980480 q^{62} - 4730963904 q^{64} - 839028480 q^{65} - 7472960920 q^{66} + 588125502 q^{67} + 6101561768 q^{68} + 7723829760 q^{70} - 10021483928 q^{72} + 1194291138 q^{73} - 7669373280 q^{74} - 221476850 q^{75} + 7187666712 q^{76} + 7176312000 q^{78} - 6408629760 q^{80} + 4396660573 q^{81} - 2429852748 q^{82} + 1949474078 q^{83} - 2916218880 q^{84} - 3841359172 q^{86} + 9008033808 q^{88} - 4953423262 q^{89} + 12545940960 q^{90} + 7645985280 q^{91} - 8903892480 q^{92} - 14182177920 q^{94} + 24050761792 q^{96} - 19570841550 q^{97} + 25720660330 q^{98} - 30528237382 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8.11.d.a 8.d 8.d $1$ $5.083$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-32\) \(-482\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{5}q^{2}-482q^{3}+2^{10}q^{4}+15424q^{6}+\cdots\)
8.11.d.b 8.d 8.d $8$ $5.083$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(42\) \(480\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(5-\beta _{1})q^{2}+(60+\beta _{1}+\beta _{2})q^{3}+(5^{2}+\cdots)q^{4}+\cdots\)