# Properties

 Label 83.13 Level 83 Weight 13 Dimension 3403 Nonzero newspaces 2 Sturm bound 7462 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$83$$ Weight: $$k$$ = $$13$$ Nonzero newspaces: $$2$$ Sturm bound: $$7462$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{13}(\Gamma_1(83))$$.

Total New Old
Modular forms 3485 3485 0
Cusp forms 3403 3403 0
Eisenstein series 82 82 0

## Trace form

 $$3403 q - 41 q^{2} - 41 q^{3} - 41 q^{4} - 41 q^{5} - 41 q^{6} - 41 q^{7} - 41 q^{8} - 41 q^{9} + O(q^{10})$$ $$3403 q - 41 q^{2} - 41 q^{3} - 41 q^{4} - 41 q^{5} - 41 q^{6} - 41 q^{7} - 41 q^{8} - 41 q^{9} - 41 q^{10} - 41 q^{11} - 41 q^{12} - 41 q^{13} - 41 q^{14} - 41 q^{15} - 41 q^{16} - 41 q^{17} - 41 q^{18} - 41 q^{19} - 41 q^{20} - 41 q^{21} - 41 q^{22} - 41 q^{23} - 41 q^{24} - 41 q^{25} - 41 q^{26} - 41 q^{27} - 41 q^{28} - 41 q^{29} - 41 q^{30} - 41 q^{31} - 41 q^{32} - 41 q^{33} - 41 q^{34} - 41 q^{35} - 41 q^{36} - 41 q^{37} - 41 q^{38} - 41 q^{39} - 41 q^{40} - 41 q^{41} - 41 q^{42} - 41 q^{43} - 41 q^{44} - 41 q^{45} - 41 q^{46} - 41 q^{47} - 41 q^{48} - 41 q^{49} - 41 q^{50} - 41 q^{51} - 41 q^{52} - 41 q^{53} - 41 q^{54} - 41 q^{55} - 41 q^{56} - 41 q^{57} - 41 q^{58} - 41 q^{59} - 41 q^{60} - 41 q^{61} - 41 q^{62} - 41 q^{63} - 41 q^{64} - 41 q^{65} + 2068916310999 q^{66} - 1100569186121 q^{67} + 1449032417239 q^{68} + 2509361228359 q^{69} + 564553515991 q^{70} - 639644821241 q^{71} - 7978148147241 q^{72} - 934353519881 q^{73} + 815966806999 q^{74} + 6196886311575 q^{75} + 3394295562199 q^{76} + 973912651879 q^{77} - 4183212812841 q^{78} - 3051933731321 q^{79} - 11783900344361 q^{80} - 3188749822761 q^{81} + 2706611988919 q^{83} + 18339336683438 q^{84} + 4716077479303 q^{85} + 3723712312279 q^{86} - 904595306601 q^{87} - 14830205644841 q^{88} - 6897811405001 q^{89} - 22098454942761 q^{90} - 3143189940521 q^{91} + 3556562042839 q^{92} + 19719816356199 q^{93} + 7340698252759 q^{94} + 7677041050183 q^{95} - 5836762624041 q^{96} - 4391492497961 q^{97} - 23832141189161 q^{98} - 6109055228681 q^{99} + O(q^{100})$$

## Decomposition of $$S_{13}^{\mathrm{new}}(\Gamma_1(83))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
83.13.b $$\chi_{83}(82, \cdot)$$ 83.13.b.a 1 1
83.13.b.b 2
83.13.b.c 80
83.13.d $$\chi_{83}(2, \cdot)$$ n/a 3320 40

"n/a" means that newforms for that character have not been added to the database yet