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Properties

Label 8.23.d
Level $8$
Weight $23$
Character orbit 8.d
Rep. character $\chi_{8}(3,\cdot)$
Character field $\Q$
Dimension $21$
Newform subspaces $2$
Sturm bound $23$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 23 \)
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: \(23\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(8, [\chi])\).

Total New Old
Modular forms 23 23 0
Cusp forms 21 21 0
Eisenstein series 2 2 0

Trace form

\( 21 q - 1542 q^{2} - 2 q^{3} - 3475692 q^{4} - 99530852 q^{6} + 3057451512 q^{8} + 198746710855 q^{9} + O(q^{10}) \) \( 21 q - 1542 q^{2} - 2 q^{3} - 3475692 q^{4} - 99530852 q^{6} + 3057451512 q^{8} + 198746710855 q^{9} + 247652816640 q^{10} + 429060198702 q^{11} + 358828301272 q^{12} + 1474757253504 q^{14} - 24971347390704 q^{16} - 13355190387798 q^{17} + 3010642073470 q^{18} + 210162440121246 q^{19} + 204774731824320 q^{20} + 1423846890409212 q^{22} - 7668805783818608 q^{24} - 6914373818310915 q^{25} - 7386019225479936 q^{26} + 9302680384061788 q^{27} + 20542005802450560 q^{28} + 54404707108487040 q^{30} - 19398127513004832 q^{32} + 23233924323553652 q^{33} - 108230334678859788 q^{34} - 195939730064275200 q^{35} - 66908565339301796 q^{36} - 740948831041341732 q^{38} + 1200834320159564160 q^{40} + 166060733460465882 q^{41} + 1887333984564111360 q^{42} + 815675000227505454 q^{43} - 1207884110470658664 q^{44} + 714483666628550784 q^{46} - 3075177644597879072 q^{48} - 8432605883853830043 q^{49} - 2716659641431952310 q^{50} + 1233388519120965116 q^{51} + 14162647107803776320 q^{52} + 31899573626383713784 q^{54} - 12215079904984655616 q^{56} + 6901474919996990228 q^{57} - 37130086609381804800 q^{58} - 88326522791660407794 q^{59} + 18180360293571100800 q^{60} - 89235754404210547200 q^{62} + 173800887342746461248 q^{64} - 3323620613445148800 q^{65} + 327905224680923205416 q^{66} + 52499977917526556862 q^{67} - 161555636496659306712 q^{68} - 44793004768252961280 q^{70} - 158726864249705903960 q^{72} - 727708336134861082182 q^{73} - 152140207109356774656 q^{74} - 305608487311643080850 q^{75} + 131275416963074184792 q^{76} + 1375632250442991066240 q^{78} - 172346045003908796160 q^{80} + 2461794604303857814777 q^{81} - 2817949347846159432108 q^{82} + 2454808555456320558558 q^{83} + 3928761998855518775040 q^{84} - 2718802965658177687812 q^{86} - 2085170096097821532912 q^{88} + 893125960879334512026 q^{89} + 1779978886121379191040 q^{90} - 14262453704073627078912 q^{91} - 11607403040451479744640 q^{92} - 9073615822553784066816 q^{94} + 13684533955754647409728 q^{96} + 4411094374114023992586 q^{97} + 10720790107023116795802 q^{98} + 48879058467615263014970 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{23}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8.23.d.a 8.d 8.d $1$ $24.537$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-2048\) \(-199058\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{11}q^{2}-199058q^{3}+2^{22}q^{4}+\cdots\)
8.23.d.b 8.d 8.d $20$ $24.537$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(506\) \(199056\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(5^{2}+\beta _{1})q^{2}+(9955-6\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)