# Properties

 Label 2205.4 Level 2205 Weight 4 Dimension 352475 Nonzero newspaces 60 Sturm bound 1354752 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$2205 = 3^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$60$$ Sturm bound: $$1354752$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2205))$$.

Total New Old
Modular forms 511872 355093 156779
Cusp forms 504192 352475 151717
Eisenstein series 7680 2618 5062

## Trace form

 $$352475 q - 92 q^{2} - 122 q^{3} - 60 q^{4} - 105 q^{5} - 394 q^{6} - 60 q^{7} - 342 q^{8} - 154 q^{9} + O(q^{10})$$ $$352475 q - 92 q^{2} - 122 q^{3} - 60 q^{4} - 105 q^{5} - 394 q^{6} - 60 q^{7} - 342 q^{8} - 154 q^{9} - 371 q^{10} - 146 q^{11} + 248 q^{12} + 382 q^{13} + 996 q^{14} - 287 q^{15} - 628 q^{16} - 1496 q^{17} - 1904 q^{18} - 2534 q^{19} - 2353 q^{20} - 1152 q^{21} - 2304 q^{22} - 402 q^{23} - 798 q^{24} + 1241 q^{25} + 3982 q^{26} + 1768 q^{27} + 3324 q^{28} + 3146 q^{29} + 1544 q^{30} + 4700 q^{31} + 6812 q^{32} + 1340 q^{33} + 888 q^{34} - 1374 q^{35} - 3782 q^{36} - 2080 q^{37} - 9860 q^{38} - 5150 q^{39} - 3757 q^{40} - 8932 q^{41} - 5556 q^{42} - 6812 q^{43} - 15754 q^{44} - 37 q^{45} - 14390 q^{46} - 842 q^{47} - 5470 q^{48} - 4032 q^{49} - 956 q^{50} - 3514 q^{51} + 13994 q^{52} + 7684 q^{53} + 4838 q^{54} + 9481 q^{55} + 16200 q^{56} + 3130 q^{57} + 4742 q^{58} + 15826 q^{59} + 13976 q^{60} - 786 q^{61} + 20166 q^{62} + 10272 q^{63} - 8606 q^{64} - 182 q^{65} + 25588 q^{66} - 5400 q^{67} + 26768 q^{68} + 21186 q^{69} - 3813 q^{70} + 8294 q^{71} - 6438 q^{72} + 8164 q^{73} - 20278 q^{74} - 17219 q^{75} - 6332 q^{76} - 17712 q^{77} - 56284 q^{78} - 17364 q^{79} - 21514 q^{80} - 25306 q^{81} - 9248 q^{82} - 10806 q^{83} - 20664 q^{84} - 3299 q^{85} - 34358 q^{86} - 24002 q^{87} - 38970 q^{88} - 35400 q^{89} - 18404 q^{90} - 21174 q^{91} - 21600 q^{92} + 6966 q^{93} - 22188 q^{94} + 1693 q^{95} + 38968 q^{96} + 19910 q^{97} - 12624 q^{98} + 43834 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2205))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2205.4.a $$\chi_{2205}(1, \cdot)$$ 2205.4.a.a 1 1
2205.4.a.b 1
2205.4.a.c 1
2205.4.a.d 1
2205.4.a.e 1
2205.4.a.f 1
2205.4.a.g 1
2205.4.a.h 1
2205.4.a.i 1
2205.4.a.j 1
2205.4.a.k 1
2205.4.a.l 1
2205.4.a.m 1
2205.4.a.n 1
2205.4.a.o 1
2205.4.a.p 1
2205.4.a.q 1
2205.4.a.r 1
2205.4.a.s 1
2205.4.a.t 1
2205.4.a.u 2
2205.4.a.v 2
2205.4.a.w 2
2205.4.a.x 2
2205.4.a.y 2
2205.4.a.z 2
2205.4.a.ba 2
2205.4.a.bb 2
2205.4.a.bc 2
2205.4.a.bd 2
2205.4.a.be 2
2205.4.a.bf 2
2205.4.a.bg 2
2205.4.a.bh 2
2205.4.a.bi 3
2205.4.a.bj 3
2205.4.a.bk 3
2205.4.a.bl 3
2205.4.a.bm 3
2205.4.a.bn 4
2205.4.a.bo 4
2205.4.a.bp 4
2205.4.a.bq 4
2205.4.a.br 5
2205.4.a.bs 5
2205.4.a.bt 5
2205.4.a.bu 5
2205.4.a.bv 5
2205.4.a.bw 5
2205.4.a.bx 6
2205.4.a.by 6
2205.4.a.bz 6
2205.4.a.ca 6
2205.4.a.cb 8
2205.4.a.cc 8
2205.4.a.cd 8
2205.4.a.ce 8
2205.4.a.cf 8
2205.4.a.cg 8
2205.4.a.ch 12
2205.4.a.ci 12
2205.4.b $$\chi_{2205}(881, \cdot)$$ n/a 160 1
2205.4.d $$\chi_{2205}(1324, \cdot)$$ n/a 302 1
2205.4.g $$\chi_{2205}(2204, \cdot)$$ n/a 240 1
2205.4.i $$\chi_{2205}(736, \cdot)$$ n/a 984 2
2205.4.j $$\chi_{2205}(226, \cdot)$$ n/a 400 2
2205.4.k $$\chi_{2205}(961, \cdot)$$ n/a 960 2
2205.4.l $$\chi_{2205}(1096, \cdot)$$ n/a 960 2
2205.4.m $$\chi_{2205}(197, \cdot)$$ n/a 492 2
2205.4.p $$\chi_{2205}(1567, \cdot)$$ n/a 592 2
2205.4.r $$\chi_{2205}(214, \cdot)$$ n/a 1424 2
2205.4.t $$\chi_{2205}(1391, \cdot)$$ n/a 960 2
2205.4.u $$\chi_{2205}(374, \cdot)$$ n/a 1424 2
2205.4.z $$\chi_{2205}(734, \cdot)$$ n/a 1424 2
2205.4.bb $$\chi_{2205}(1844, \cdot)$$ n/a 480 2
2205.4.be $$\chi_{2205}(1256, \cdot)$$ n/a 960 2
2205.4.bf $$\chi_{2205}(1549, \cdot)$$ n/a 592 2
2205.4.bh $$\chi_{2205}(589, \cdot)$$ n/a 1456 2
2205.4.bj $$\chi_{2205}(521, \cdot)$$ n/a 320 2
2205.4.bl $$\chi_{2205}(146, \cdot)$$ n/a 960 2
2205.4.bo $$\chi_{2205}(79, \cdot)$$ n/a 1424 2
2205.4.bq $$\chi_{2205}(509, \cdot)$$ n/a 1424 2
2205.4.bs $$\chi_{2205}(316, \cdot)$$ n/a 1680 6
2205.4.bt $$\chi_{2205}(178, \cdot)$$ n/a 2848 4
2205.4.bw $$\chi_{2205}(263, \cdot)$$ n/a 2848 4
2205.4.by $$\chi_{2205}(128, \cdot)$$ n/a 2848 4
2205.4.ca $$\chi_{2205}(1207, \cdot)$$ n/a 1184 4
2205.4.cc $$\chi_{2205}(97, \cdot)$$ n/a 2848 4
2205.4.cd $$\chi_{2205}(932, \cdot)$$ n/a 2912 4
2205.4.cf $$\chi_{2205}(422, \cdot)$$ n/a 960 4
2205.4.ch $$\chi_{2205}(313, \cdot)$$ n/a 2848 4
2205.4.ck $$\chi_{2205}(314, \cdot)$$ n/a 2016 6
2205.4.cn $$\chi_{2205}(64, \cdot)$$ n/a 2508 6
2205.4.cp $$\chi_{2205}(251, \cdot)$$ n/a 1344 6
2205.4.cq $$\chi_{2205}(121, \cdot)$$ n/a 8064 12
2205.4.cr $$\chi_{2205}(16, \cdot)$$ n/a 8064 12
2205.4.cs $$\chi_{2205}(46, \cdot)$$ n/a 3360 12
2205.4.ct $$\chi_{2205}(106, \cdot)$$ n/a 8064 12
2205.4.cv $$\chi_{2205}(118, \cdot)$$ n/a 5016 12
2205.4.cw $$\chi_{2205}(8, \cdot)$$ n/a 4032 12
2205.4.cz $$\chi_{2205}(164, \cdot)$$ n/a 12048 12
2205.4.db $$\chi_{2205}(4, \cdot)$$ n/a 12048 12
2205.4.de $$\chi_{2205}(41, \cdot)$$ n/a 8064 12
2205.4.dg $$\chi_{2205}(26, \cdot)$$ n/a 2688 12
2205.4.di $$\chi_{2205}(169, \cdot)$$ n/a 12048 12
2205.4.dk $$\chi_{2205}(109, \cdot)$$ n/a 5016 12
2205.4.dl $$\chi_{2205}(236, \cdot)$$ n/a 8064 12
2205.4.do $$\chi_{2205}(89, \cdot)$$ n/a 4032 12
2205.4.dq $$\chi_{2205}(104, \cdot)$$ n/a 12048 12
2205.4.dv $$\chi_{2205}(59, \cdot)$$ n/a 12048 12
2205.4.dw $$\chi_{2205}(101, \cdot)$$ n/a 8064 12
2205.4.dy $$\chi_{2205}(184, \cdot)$$ n/a 12048 12
2205.4.ea $$\chi_{2205}(157, \cdot)$$ n/a 24096 24
2205.4.ec $$\chi_{2205}(92, \cdot)$$ n/a 24096 24
2205.4.ee $$\chi_{2205}(53, \cdot)$$ n/a 8064 24
2205.4.eh $$\chi_{2205}(73, \cdot)$$ n/a 10032 24
2205.4.ej $$\chi_{2205}(13, \cdot)$$ n/a 24096 24
2205.4.el $$\chi_{2205}(2, \cdot)$$ n/a 24096 24
2205.4.en $$\chi_{2205}(23, \cdot)$$ n/a 24096 24
2205.4.eo $$\chi_{2205}(52, \cdot)$$ n/a 24096 24

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2205))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(2205)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(315))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(441))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(735))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2205))$$$$^{\oplus 1}$$