# Properties

 Label 91.8.ba Level $91$ Weight $8$ Character orbit 91.ba Rep. character $\chi_{91}(45,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $252$ Newform subspaces $1$ Sturm bound $74$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$91 = 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 91.ba (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$1$$ Sturm bound: $$74$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(91, [\chi])$$.

Total New Old
Modular forms 268 268 0
Cusp forms 252 252 0
Eisenstein series 16 16 0

## Trace form

 $$252 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 768 q^{6} + 2962 q^{7} + 248 q^{8} + 84566 q^{9} + O(q^{10})$$ $$252 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 768 q^{6} + 2962 q^{7} + 248 q^{8} + 84566 q^{9} - 6 q^{10} + 146 q^{11} + 13824 q^{12} + 29800 q^{14} + 7978 q^{15} - 884740 q^{16} - 12 q^{17} + 88466 q^{18} - 25858 q^{19} + 99072 q^{20} - 46206 q^{21} + 8028 q^{22} - 200106 q^{24} - 409476 q^{26} - 744574 q^{28} - 116432 q^{29} + 807738 q^{30} + 340196 q^{31} + 760882 q^{32} + 132036 q^{33} - 768 q^{34} - 828764 q^{35} - 868554 q^{36} + 1579302 q^{37} + 1237892 q^{39} - 3275952 q^{40} + 2417670 q^{41} - 1233382 q^{42} + 2599008 q^{43} + 103470 q^{44} - 6 q^{45} + 3132684 q^{46} - 6 q^{47} + 72060 q^{48} + 2810758 q^{49} - 5631014 q^{50} + 3461940 q^{51} - 2388230 q^{52} - 2003916 q^{53} - 4265382 q^{54} + 2590062 q^{55} + 5277690 q^{56} + 8114044 q^{57} + 10279662 q^{58} + 2753898 q^{59} + 2401274 q^{60} + 8212710 q^{61} - 5434848 q^{62} - 10063762 q^{63} + 381604 q^{65} - 11087430 q^{66} + 157462 q^{67} - 7796922 q^{69} + 8057556 q^{70} - 25883586 q^{71} + 6336142 q^{72} - 3413048 q^{73} - 17821116 q^{74} + 11812488 q^{75} + 11124992 q^{76} + 50057426 q^{78} - 8377948 q^{79} - 40902090 q^{80} - 44505350 q^{81} - 29444742 q^{82} + 14652858 q^{83} - 27464732 q^{84} - 42392038 q^{85} - 26640894 q^{86} + 55640514 q^{88} - 18684288 q^{89} + 57369384 q^{90} + 51684386 q^{91} + 95785908 q^{92} + 62946972 q^{93} - 4391034 q^{94} - 27292422 q^{96} - 10736774 q^{97} - 101916752 q^{98} + 12081580 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(91, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.8.ba.a $252$ $28.427$ None $$-2$$ $$-6$$ $$-6$$ $$2962$$