# Properties

 Label 11.3 Level 11 Weight 3 Dimension 5 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 30 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$11\( 11$$ \) Weight: $$k$$ = $$3$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$30$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(11))$$.

Total New Old
Modular forms 15 15 0
Cusp forms 5 5 0
Eisenstein series 10 10 0

## Trace form

 $$5q - 5q^{2} - 5q^{3} - 5q^{4} - 5q^{5} + 15q^{6} + 10q^{7} + 15q^{8} + 5q^{9} + O(q^{10})$$ $$5q - 5q^{2} - 5q^{3} - 5q^{4} - 5q^{5} + 15q^{6} + 10q^{7} + 15q^{8} + 5q^{9} - 10q^{11} - 50q^{12} - 20q^{13} - 10q^{14} + 5q^{15} + 35q^{16} + 30q^{18} + 25q^{19} + 40q^{20} - 35q^{22} + 15q^{23} + 5q^{24} - 15q^{25} - 10q^{26} - 20q^{27} - 60q^{28} - 40q^{29} - 80q^{30} - 95q^{31} + 120q^{33} + 130q^{34} + 80q^{35} + 90q^{36} + 65q^{37} - 60q^{38} + 50q^{39} - 60q^{40} - 80q^{41} - 10q^{42} - 20q^{44} - 40q^{45} + 30q^{46} + 20q^{47} - 120q^{48} - 60q^{49} - 45q^{50} - 195q^{51} + 110q^{52} + 50q^{53} - 65q^{55} + 100q^{56} + 45q^{57} + 40q^{58} + 130q^{59} + 160q^{60} + 10q^{61} + 200q^{62} + 90q^{63} - 85q^{64} + 90q^{66} - 195q^{67} - 260q^{68} - 185q^{69} - 40q^{70} + 15q^{71} - 95q^{72} + 300q^{73} - 270q^{74} + 165q^{75} - 200q^{77} - 200q^{78} + 70q^{79} - 100q^{80} - 85q^{81} + 25q^{82} + 225q^{83} + 90q^{84} + 260q^{85} + 175q^{86} + 55q^{88} + 25q^{89} - 20q^{90} - 80q^{91} + 180q^{92} - 15q^{93} + 120q^{94} - 100q^{95} + 340q^{96} - 70q^{97} - 145q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(11))$$

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
11.3.b $$\chi_{11}(10, \cdot)$$ 11.3.b.a 1 1
11.3.d $$\chi_{11}(2, \cdot)$$ 11.3.d.a 4 4

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 - 2 T )( 1 + 2 T )$$)($$1 + 5 T + 19 T^{2} + 55 T^{3} + 121 T^{4} + 220 T^{5} + 304 T^{6} + 320 T^{7} + 256 T^{8}$$)
$3$ ($$1 + 5 T + 9 T^{2}$$)($$1 + T^{2} - 20 T^{3} + 61 T^{4} - 180 T^{5} + 81 T^{6} + 6561 T^{8}$$)
$5$ ($$1 + T + 25 T^{2}$$)($$1 + 4 T - 9 T^{2} - 136 T^{3} - 319 T^{4} - 3400 T^{5} - 5625 T^{6} + 62500 T^{7} + 390625 T^{8}$$)
$7$ ($$( 1 - 7 T )( 1 + 7 T )$$)($$1 - 10 T + 129 T^{2} - 1310 T^{3} + 8361 T^{4} - 64190 T^{5} + 309729 T^{6} - 1176490 T^{7} + 5764801 T^{8}$$)
$11$ ($$1 + 11 T$$)($$1 - T - 209 T^{2} - 121 T^{3} + 14641 T^{4}$$)
$13$ ($$( 1 - 13 T )( 1 + 13 T )$$)($$1 + 20 T + 369 T^{2} + 6070 T^{3} + 81261 T^{4} + 1025830 T^{5} + 10539009 T^{6} + 96536180 T^{7} + 815730721 T^{8}$$)
$17$ ($$( 1 - 17 T )( 1 + 17 T )$$)($$1 + 289 T^{2} + 7800 T^{3} - 17879 T^{4} + 2254200 T^{5} + 24137569 T^{6} + 6975757441 T^{8}$$)
$19$ ($$( 1 - 19 T )( 1 + 19 T )$$)($$1 - 25 T + 561 T^{2} - 5855 T^{3} + 141756 T^{4} - 2113655 T^{5} + 73110081 T^{6} - 1176147025 T^{7} + 16983563041 T^{8}$$)
$23$ ($$1 - 35 T + 529 T^{2}$$)($$( 1 + 10 T + 1078 T^{2} + 5290 T^{3} + 279841 T^{4} )^{2}$$)
$29$ ($$( 1 - 29 T )( 1 + 29 T )$$)($$1 + 40 T + 1881 T^{2} + 81410 T^{3} + 2180301 T^{4} + 68465810 T^{5} + 1330395561 T^{6} + 23792932840 T^{7} + 500246412961 T^{8}$$)
$31$ ($$1 + 37 T + 961 T^{2}$$)($$1 + 58 T + 423 T^{2} - 17434 T^{3} - 243175 T^{4} - 16754074 T^{5} + 390649383 T^{6} + 51475213498 T^{7} + 852891037441 T^{8}$$)
$37$ ($$1 + 25 T + 1369 T^{2}$$)($$1 - 90 T + 3491 T^{2} - 145800 T^{3} + 6716341 T^{4} - 199600200 T^{5} + 6542696051 T^{6} - 230915376810 T^{7} + 3512479453921 T^{8}$$)
$41$ ($$( 1 - 41 T )( 1 + 41 T )$$)($$1 + 80 T + 6401 T^{2} + 349320 T^{3} + 15534121 T^{4} + 587206920 T^{5} + 18087696161 T^{6} + 380008339280 T^{7} + 7984925229121 T^{8}$$)
$43$ ($$( 1 - 43 T )( 1 + 43 T )$$)($$1 - 5771 T^{2} + 15084961 T^{4} - 19729900571 T^{6} + 11688200277601 T^{8}$$)
$47$ ($$1 - 50 T + 2209 T^{2}$$)($$1 + 30 T - 1569 T^{2} - 98050 T^{3} + 581001 T^{4} - 216592450 T^{5} - 7656219489 T^{6} + 323376459870 T^{7} + 23811286661761 T^{8}$$)
$53$ ($$1 + 70 T + 2809 T^{2}$$)($$1 - 120 T + 2591 T^{2} + 279810 T^{3} - 24164819 T^{4} + 785986290 T^{5} + 20444236271 T^{6} - 2659723335480 T^{7} + 62259690411361 T^{8}$$)
$59$ ($$1 - 107 T + 3481 T^{2}$$)($$1 - 23 T - 2427 T^{2} - 104641 T^{3} + 14691380 T^{4} - 364255321 T^{5} - 29408835147 T^{6} - 970152273743 T^{7} + 146830437604321 T^{8}$$)
$61$ ($$( 1 - 61 T )( 1 + 61 T )$$)($$1 - 10 T + 3601 T^{2} + 243430 T^{3} + 7253641 T^{4} + 905803030 T^{5} + 49858873441 T^{6} - 515203743610 T^{7} + 191707312997281 T^{8}$$)
$67$ ($$1 - 35 T + 4489 T^{2}$$)($$( 1 + 115 T + 11923 T^{2} + 516235 T^{3} + 20151121 T^{4} )^{2}$$)
$71$ ($$1 + 133 T + 5041 T^{2}$$)($$1 - 148 T + 9423 T^{2} - 841046 T^{3} + 82451165 T^{4} - 4239712886 T^{5} + 239454270063 T^{6} - 18958842020308 T^{7} + 645753531245761 T^{8}$$)
$73$ ($$( 1 - 73 T )( 1 + 73 T )$$)($$1 - 300 T + 46429 T^{2} - 5018400 T^{3} + 415041241 T^{4} - 26743053600 T^{5} + 1318501931389 T^{6} - 45400267886700 T^{7} + 806460091894081 T^{8}$$)
$79$ ($$( 1 - 79 T )( 1 + 79 T )$$)($$1 - 70 T + 10021 T^{2} - 1216880 T^{3} + 75589621 T^{4} - 7594548080 T^{5} + 390318761701 T^{6} - 17016121886470 T^{7} + 1517108809906561 T^{8}$$)
$83$ ($$( 1 - 83 T )( 1 + 83 T )$$)($$1 - 225 T + 27589 T^{2} - 2589975 T^{3} + 221504596 T^{4} - 17842337775 T^{5} + 1309327618069 T^{6} - 73561584008025 T^{7} + 2252292232139041 T^{8}$$)
$89$ ($$1 + 97 T + 7921 T^{2}$$)($$( 1 - 61 T + 8161 T^{2} - 483181 T^{3} + 62742241 T^{4} )^{2}$$)
$97$ ($$1 - 95 T + 9409 T^{2}$$)($$1 + 165 T + 7431 T^{2} + 999895 T^{3} + 180445176 T^{4} + 9408012055 T^{5} + 657861087111 T^{6} + 137440380813285 T^{7} + 7837433594376961 T^{8}$$)