# Properties

 Label 23.10 Level 23 Weight 10 Dimension 187 Nonzero newspaces 2 Newforms 3 Sturm bound 440 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$23$$ Weight: $$k$$ = $$10$$ Nonzero newspaces: $$2$$ Newforms: $$3$$ Sturm bound: $$440$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{10}(\Gamma_1(23))$$.

Total New Old
Modular forms 209 207 2
Cusp forms 187 187 0
Eisenstein series 22 20 2

## Trace form

 $$187q$$ $$\mathstrut -\mathstrut 11q^{2}$$ $$\mathstrut -\mathstrut 11q^{3}$$ $$\mathstrut -\mathstrut 11q^{4}$$ $$\mathstrut -\mathstrut 11q^{5}$$ $$\mathstrut -\mathstrut 11q^{6}$$ $$\mathstrut -\mathstrut 11q^{7}$$ $$\mathstrut -\mathstrut 11q^{8}$$ $$\mathstrut -\mathstrut 11q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$187q$$ $$\mathstrut -\mathstrut 11q^{2}$$ $$\mathstrut -\mathstrut 11q^{3}$$ $$\mathstrut -\mathstrut 11q^{4}$$ $$\mathstrut -\mathstrut 11q^{5}$$ $$\mathstrut -\mathstrut 11q^{6}$$ $$\mathstrut -\mathstrut 11q^{7}$$ $$\mathstrut -\mathstrut 11q^{8}$$ $$\mathstrut -\mathstrut 11q^{9}$$ $$\mathstrut -\mathstrut 11q^{10}$$ $$\mathstrut -\mathstrut 11q^{11}$$ $$\mathstrut -\mathstrut 11q^{12}$$ $$\mathstrut -\mathstrut 11q^{13}$$ $$\mathstrut -\mathstrut 11q^{14}$$ $$\mathstrut +\mathstrut 969023q^{15}$$ $$\mathstrut -\mathstrut 478731q^{16}$$ $$\mathstrut -\mathstrut 1054867q^{17}$$ $$\mathstrut +\mathstrut 1519925q^{18}$$ $$\mathstrut +\mathstrut 1526459q^{19}$$ $$\mathstrut +\mathstrut 3198965q^{20}$$ $$\mathstrut -\mathstrut 3575231q^{21}$$ $$\mathstrut -\mathstrut 5153654q^{22}$$ $$\mathstrut -\mathstrut 3650823q^{23}$$ $$\mathstrut +\mathstrut 6167018q^{24}$$ $$\mathstrut +\mathstrut 8299797q^{25}$$ $$\mathstrut +\mathstrut 9664149q^{26}$$ $$\mathstrut +\mathstrut 3875311q^{27}$$ $$\mathstrut -\mathstrut 21469195q^{28}$$ $$\mathstrut -\mathstrut 10200751q^{29}$$ $$\mathstrut -\mathstrut 24330955q^{30}$$ $$\mathstrut +\mathstrut 9969839q^{31}$$ $$\mathstrut +\mathstrut 46627317q^{32}$$ $$\mathstrut -\mathstrut 21902947q^{33}$$ $$\mathstrut -\mathstrut 8377589q^{34}$$ $$\mathstrut +\mathstrut 57736239q^{35}$$ $$\mathstrut -\mathstrut 30672686q^{36}$$ $$\mathstrut -\mathstrut 107778935q^{37}$$ $$\mathstrut -\mathstrut 92052576q^{38}$$ $$\mathstrut +\mathstrut 23347753q^{39}$$ $$\mathstrut +\mathstrut 213344989q^{40}$$ $$\mathstrut +\mathstrut 62844639q^{41}$$ $$\mathstrut +\mathstrut 178280179q^{42}$$ $$\mathstrut -\mathstrut 29184023q^{43}$$ $$\mathstrut -\mathstrut 225229796q^{44}$$ $$\mathstrut -\mathstrut 270641272q^{45}$$ $$\mathstrut -\mathstrut 311125331q^{46}$$ $$\mathstrut -\mathstrut 54389346q^{47}$$ $$\mathstrut +\mathstrut 183376413q^{48}$$ $$\mathstrut +\mathstrut 341786995q^{49}$$ $$\mathstrut +\mathstrut 511328114q^{50}$$ $$\mathstrut +\mathstrut 237700969q^{51}$$ $$\mathstrut +\mathstrut 138729679q^{52}$$ $$\mathstrut -\mathstrut 103750977q^{53}$$ $$\mathstrut -\mathstrut 1104475251q^{54}$$ $$\mathstrut -\mathstrut 96640643q^{55}$$ $$\mathstrut +\mathstrut 210507990q^{56}$$ $$\mathstrut +\mathstrut 59318281q^{57}$$ $$\mathstrut +\mathstrut 513967300q^{58}$$ $$\mathstrut -\mathstrut 118047545q^{59}$$ $$\mathstrut -\mathstrut 1153719721q^{60}$$ $$\mathstrut +\mathstrut 344711653q^{61}$$ $$\mathstrut +\mathstrut 980989141q^{62}$$ $$\mathstrut +\mathstrut 882717759q^{63}$$ $$\mathstrut +\mathstrut 986185717q^{64}$$ $$\mathstrut +\mathstrut 158418557q^{65}$$ $$\mathstrut -\mathstrut 747426636q^{66}$$ $$\mathstrut -\mathstrut 378627887q^{67}$$ $$\mathstrut -\mathstrut 2822341654q^{68}$$ $$\mathstrut -\mathstrut 1069913031q^{69}$$ $$\mathstrut -\mathstrut 1006270870q^{70}$$ $$\mathstrut +\mathstrut 56718519q^{71}$$ $$\mathstrut +\mathstrut 1971614260q^{72}$$ $$\mathstrut +\mathstrut 582788437q^{73}$$ $$\mathstrut +\mathstrut 699926392q^{74}$$ $$\mathstrut +\mathstrut 3594630963q^{75}$$ $$\mathstrut +\mathstrut 4934994042q^{76}$$ $$\mathstrut +\mathstrut 832730437q^{77}$$ $$\mathstrut -\mathstrut 4315286437q^{78}$$ $$\mathstrut -\mathstrut 4249645807q^{79}$$ $$\mathstrut -\mathstrut 10615143550q^{80}$$ $$\mathstrut -\mathstrut 5321334799q^{81}$$ $$\mathstrut +\mathstrut 416976439q^{82}$$ $$\mathstrut +\mathstrut 3425248739q^{83}$$ $$\mathstrut +\mathstrut 14370912435q^{84}$$ $$\mathstrut +\mathstrut 7253042687q^{85}$$ $$\mathstrut +\mathstrut 779636011q^{86}$$ $$\mathstrut +\mathstrut 2829378673q^{87}$$ $$\mathstrut -\mathstrut 671992739q^{88}$$ $$\mathstrut -\mathstrut 2402723741q^{89}$$ $$\mathstrut -\mathstrut 12214147682q^{90}$$ $$\mathstrut -\mathstrut 6034596590q^{91}$$ $$\mathstrut -\mathstrut 6333894578q^{92}$$ $$\mathstrut -\mathstrut 5895816058q^{93}$$ $$\mathstrut -\mathstrut 1344916188q^{94}$$ $$\mathstrut -\mathstrut 1504040945q^{95}$$ $$\mathstrut +\mathstrut 17191683300q^{96}$$ $$\mathstrut +\mathstrut 11525413603q^{97}$$ $$\mathstrut +\mathstrut 12597404941q^{98}$$ $$\mathstrut +\mathstrut 10210410199q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{10}^{\mathrm{new}}(\Gamma_1(23))$$

We only show spaces with even 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
23.10.a $$\chi_{23}(1, \cdot)$$ 23.10.a.a 7 1
23.10.a.b 10
23.10.c $$\chi_{23}(2, \cdot)$$ 23.10.c.a 170 10