# Properties

 Label 1305.2 Level 1305 Weight 2 Dimension 43056 Nonzero newspaces 40 Sturm bound 241920 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$1305 = 3^{2} \cdot 5 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$241920$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1305))$$.

Total New Old
Modular forms 62272 44516 17756
Cusp forms 58689 43056 15633
Eisenstein series 3583 1460 2123

## Trace form

 $$43056 q - 70 q^{2} - 96 q^{3} - 62 q^{4} - 108 q^{5} - 304 q^{6} - 60 q^{7} - 78 q^{8} - 104 q^{9} + O(q^{10})$$ $$43056 q - 70 q^{2} - 96 q^{3} - 62 q^{4} - 108 q^{5} - 304 q^{6} - 60 q^{7} - 78 q^{8} - 104 q^{9} - 348 q^{10} - 244 q^{11} - 128 q^{12} - 80 q^{13} - 108 q^{14} - 176 q^{15} - 238 q^{16} - 88 q^{17} - 144 q^{18} - 212 q^{19} - 155 q^{20} - 336 q^{21} - 44 q^{22} - 80 q^{23} - 184 q^{24} - 104 q^{25} - 210 q^{26} - 144 q^{27} - 128 q^{28} - 50 q^{29} - 400 q^{30} - 180 q^{31} + 2 q^{32} - 128 q^{33} - 42 q^{34} - 82 q^{35} - 272 q^{36} - 228 q^{37} + 4 q^{38} - 48 q^{39} - 59 q^{40} - 152 q^{41} - 40 q^{42} - 20 q^{43} + 80 q^{44} - 112 q^{45} - 536 q^{46} + 52 q^{47} - 32 q^{48} + 22 q^{49} + 34 q^{50} - 304 q^{51} + 136 q^{52} + 38 q^{53} - 104 q^{54} - 290 q^{55} - 272 q^{56} - 144 q^{57} + 226 q^{58} - 200 q^{59} - 208 q^{60} - 192 q^{61} - 56 q^{62} - 232 q^{63} - 98 q^{64} - 187 q^{65} - 512 q^{66} - 20 q^{67} - 28 q^{68} - 232 q^{69} - 218 q^{70} - 576 q^{71} - 496 q^{72} - 346 q^{73} - 556 q^{74} - 292 q^{75} - 996 q^{76} - 480 q^{77} - 480 q^{78} - 228 q^{79} - 644 q^{80} - 704 q^{81} - 528 q^{82} - 276 q^{83} - 640 q^{84} - 366 q^{85} - 976 q^{86} - 348 q^{87} - 1176 q^{88} - 372 q^{89} - 240 q^{90} - 1164 q^{91} - 900 q^{92} - 216 q^{93} - 412 q^{94} - 382 q^{95} - 1008 q^{96} - 158 q^{97} - 450 q^{98} - 352 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1305))$$

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
1305.2.a $$\chi_{1305}(1, \cdot)$$ 1305.2.a.a 1 1
1305.2.a.b 1
1305.2.a.c 1
1305.2.a.d 1
1305.2.a.e 1
1305.2.a.f 1
1305.2.a.g 1
1305.2.a.h 2
1305.2.a.i 2
1305.2.a.j 2
1305.2.a.k 2
1305.2.a.l 2
1305.2.a.m 2
1305.2.a.n 2
1305.2.a.o 3
1305.2.a.p 3
1305.2.a.q 3
1305.2.a.r 4
1305.2.a.s 7
1305.2.a.t 7
1305.2.c $$\chi_{1305}(784, \cdot)$$ 1305.2.c.a 2 1
1305.2.c.b 2
1305.2.c.c 2
1305.2.c.d 2
1305.2.c.e 4
1305.2.c.f 4
1305.2.c.g 4
1305.2.c.h 6
1305.2.c.i 10
1305.2.c.j 10
1305.2.c.k 12
1305.2.c.l 12
1305.2.d $$\chi_{1305}(811, \cdot)$$ 1305.2.d.a 4 1
1305.2.d.b 6
1305.2.d.c 10
1305.2.d.d 10
1305.2.d.e 10
1305.2.d.f 10
1305.2.f $$\chi_{1305}(289, \cdot)$$ 1305.2.f.a 2 1
1305.2.f.b 2
1305.2.f.c 2
1305.2.f.d 2
1305.2.f.e 4
1305.2.f.f 4
1305.2.f.g 4
1305.2.f.h 4
1305.2.f.i 4
1305.2.f.j 4
1305.2.f.k 12
1305.2.f.l 12
1305.2.f.m 16
1305.2.i $$\chi_{1305}(436, \cdot)$$ n/a 224 2
1305.2.k $$\chi_{1305}(568, \cdot)$$ n/a 146 2
1305.2.m $$\chi_{1305}(539, \cdot)$$ n/a 120 2
1305.2.n $$\chi_{1305}(233, \cdot)$$ n/a 112 2
1305.2.q $$\chi_{1305}(782, \cdot)$$ n/a 120 2
1305.2.r $$\chi_{1305}(476, \cdot)$$ 1305.2.r.a 8 2
1305.2.r.b 8
1305.2.r.c 32
1305.2.r.d 32
1305.2.t $$\chi_{1305}(307, \cdot)$$ n/a 146 2
1305.2.w $$\chi_{1305}(724, \cdot)$$ n/a 352 2
1305.2.y $$\chi_{1305}(376, \cdot)$$ n/a 240 2
1305.2.bb $$\chi_{1305}(349, \cdot)$$ n/a 336 2
1305.2.bc $$\chi_{1305}(136, \cdot)$$ n/a 300 6
1305.2.bd $$\chi_{1305}(418, \cdot)$$ n/a 704 4
1305.2.bg $$\chi_{1305}(41, \cdot)$$ n/a 480 4
1305.2.bi $$\chi_{1305}(173, \cdot)$$ n/a 704 4
1305.2.bj $$\chi_{1305}(407, \cdot)$$ n/a 672 4
1305.2.bl $$\chi_{1305}(104, \cdot)$$ n/a 704 4
1305.2.bo $$\chi_{1305}(133, \cdot)$$ n/a 704 4
1305.2.br $$\chi_{1305}(64, \cdot)$$ n/a 432 6
1305.2.bt $$\chi_{1305}(91, \cdot)$$ n/a 300 6
1305.2.bu $$\chi_{1305}(199, \cdot)$$ n/a 444 6
1305.2.bw $$\chi_{1305}(16, \cdot)$$ n/a 1440 12
1305.2.by $$\chi_{1305}(73, \cdot)$$ n/a 876 12
1305.2.ca $$\chi_{1305}(26, \cdot)$$ n/a 480 12
1305.2.cb $$\chi_{1305}(62, \cdot)$$ n/a 720 12
1305.2.ce $$\chi_{1305}(53, \cdot)$$ n/a 720 12
1305.2.cf $$\chi_{1305}(44, \cdot)$$ n/a 720 12
1305.2.ch $$\chi_{1305}(37, \cdot)$$ n/a 876 12
1305.2.cj $$\chi_{1305}(49, \cdot)$$ n/a 2112 12
1305.2.cm $$\chi_{1305}(121, \cdot)$$ n/a 1440 12
1305.2.co $$\chi_{1305}(4, \cdot)$$ n/a 2112 12
1305.2.cq $$\chi_{1305}(43, \cdot)$$ n/a 4224 24
1305.2.ct $$\chi_{1305}(14, \cdot)$$ n/a 4224 24
1305.2.cv $$\chi_{1305}(23, \cdot)$$ n/a 4224 24
1305.2.cw $$\chi_{1305}(38, \cdot)$$ n/a 4224 24
1305.2.cy $$\chi_{1305}(11, \cdot)$$ n/a 2880 24
1305.2.db $$\chi_{1305}(292, \cdot)$$ n/a 4224 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1305))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1305)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(261))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(435))$$$$^{\oplus 2}$$