# Properties

 Label 35.23 Level 35 Weight 23 Dimension 910 Nonzero newspaces 6 Sturm bound 2208 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$35 = 5 \cdot 7$$ Weight: $$k$$ = $$23$$ Nonzero newspaces: $$6$$ Sturm bound: $$2208$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{23}(\Gamma_1(35))$$.

Total New Old
Modular forms 1080 938 142
Cusp forms 1032 910 122
Eisenstein series 48 28 20

## Trace form

 $$910q + 4094q^{2} + 286488q^{3} + 16777210q^{4} + 46650938q^{5} - 1178125704q^{6} - 6616893418q^{7} + 76070219502q^{8} - 26562038958q^{9} + O(q^{10})$$ $$910q + 4094q^{2} + 286488q^{3} + 16777210q^{4} + 46650938q^{5} - 1178125704q^{6} - 6616893418q^{7} + 76070219502q^{8} - 26562038958q^{9} + 238180325588q^{10} + 393946770568q^{11} - 4952650201812q^{12} - 108539506612q^{13} - 16684998277134q^{14} + 30401685084156q^{15} + 122087018468038q^{16} - 103894998659272q^{17} + 589659160270542q^{18} - 813078042625584q^{19} + 562120034664588q^{20} - 1673716339685940q^{21} + 1954861330689460q^{22} + 599711324455532q^{23} - 4053336729756444q^{24} + 14806243482738136q^{25} - 26965106857136720q^{26} + 19822543247097240q^{27} + 72977476593315346q^{28} - 62995068953530212q^{29} + 158449819481700516q^{30} + 307839351199095868q^{31} - 855096979998266158q^{32} + 602098718905081908q^{33} - 544379882253881798q^{35} + 2243054359283666310q^{36} + 532107966126909736q^{37} - 770425946997187164q^{38} + 912784164542508480q^{39} + 344152254314803356q^{40} + 654055225615975648q^{41} + 4049029157835777732q^{42} - 2905164801761769356q^{43} - 17817760830809248488q^{44} + 1187473765503930972q^{45} + 23621680952106174196q^{46} - 9747470751030066268q^{47} - 32074453705511824044q^{48} + 21814131162004867394q^{49} + 30319481715285917306q^{50} - 86496488451433376748q^{51} + 102548800180336143020q^{52} + 2974333597287374300q^{53} - 219815056398288546444q^{54} + 94615819650622745524q^{55} + 46032071014756498854q^{56} + 19799987577597959232q^{57} - 217857842208289366080q^{58} - 31157895334833533712q^{59} + 739879599688112011608q^{60} + 49830881761388230132q^{61} - 759992497051409061656q^{62} - 137658560599229190810q^{63} + 614698514775689169814q^{64} + 635563847390961458396q^{65} - 2336382570232614950496q^{66} + 288472815684857707596q^{67} + 2406455020322315235928q^{68} - 3867327328760744246472q^{70} + 2463126198997039558012q^{71} + 3854373790689721818894q^{72} - 3076356276934854712936q^{73} - 2608328518875550795548q^{74} + 3321502145540010338442q^{75} + 391190574723957296088q^{76} - 3103123784415349954612q^{77} - 6999053610647056928760q^{78} - 524214417094700902364q^{79} + 5596169944550543573432q^{80} + 18159393608019115015746q^{81} - 18272510883235870885172q^{82} - 17211113990329203732484q^{83} + 6084268583892086793564q^{84} + 31476686455192577369948q^{85} + 12516569176769164338196q^{86} - 31298137323358563160392q^{87} - 66477408720726213851184q^{88} + 24571163222367334481340q^{89} + 65787699802710322096200q^{90} + 11805200863223308541216q^{91} - 6650341984047739420156q^{92} - 125377558298806203404028q^{93} + 41606078292561890943444q^{94} + 50551987590698311478442q^{95} + 15087249769355067174600q^{96} + 4656456708284692337492q^{97} + 10695605096138793940686q^{98} + 4390424411369864130420q^{99} + O(q^{100})$$

## Decomposition of $$S_{23}^{\mathrm{new}}(\Gamma_1(35))$$

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
35.23.c $$\chi_{35}(34, \cdot)$$ 35.23.c.a 1 1
35.23.c.b 1
35.23.c.c 84
35.23.d $$\chi_{35}(6, \cdot)$$ 35.23.d.a 60 1
35.23.g $$\chi_{35}(8, \cdot)$$ n/a 132 2
35.23.h $$\chi_{35}(26, \cdot)$$ n/a 116 2
35.23.i $$\chi_{35}(19, \cdot)$$ n/a 172 2
35.23.l $$\chi_{35}(2, \cdot)$$ n/a 344 4

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

## Decomposition of $$S_{23}^{\mathrm{old}}(\Gamma_1(35))$$ into lower level spaces

$$S_{23}^{\mathrm{old}}(\Gamma_1(35)) \cong$$ $$S_{23}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 2}$$$$\oplus$$$$S_{23}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 2}$$