# Properties

 Label 1449.2 Level 1449 Weight 2 Dimension 56520 Nonzero newspaces 40 Sturm bound 304128 Trace bound 22

## Defining parameters

 Level: $$N$$ = $$1449 = 3^{2} \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$304128$$ Trace bound: $$22$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1449))$$.

Total New Old
Modular forms 78144 58412 19732
Cusp forms 73921 56520 17401
Eisenstein series 4223 1892 2331

## Trace form

 $$56520 q - 114 q^{2} - 152 q^{3} - 106 q^{4} - 108 q^{5} - 152 q^{6} - 139 q^{7} - 276 q^{8} - 152 q^{9} + O(q^{10})$$ $$56520 q - 114 q^{2} - 152 q^{3} - 106 q^{4} - 108 q^{5} - 152 q^{6} - 139 q^{7} - 276 q^{8} - 152 q^{9} - 312 q^{10} - 96 q^{11} - 176 q^{12} - 100 q^{13} - 159 q^{14} - 416 q^{15} - 94 q^{16} - 134 q^{17} - 200 q^{18} - 342 q^{19} - 116 q^{20} - 232 q^{21} - 264 q^{22} - 94 q^{23} - 400 q^{24} - 70 q^{25} - 136 q^{26} - 188 q^{27} - 385 q^{28} - 272 q^{29} - 236 q^{30} - 90 q^{31} - 166 q^{32} - 200 q^{33} - 112 q^{34} - 191 q^{35} - 512 q^{36} - 280 q^{37} - 130 q^{38} - 224 q^{39} - 52 q^{40} - 208 q^{41} - 328 q^{42} - 226 q^{43} - 242 q^{44} - 248 q^{45} - 244 q^{46} - 212 q^{47} - 128 q^{48} - 105 q^{49} - 158 q^{50} - 152 q^{51} + 72 q^{52} - 4 q^{53} - 180 q^{54} - 344 q^{55} - 134 q^{56} - 428 q^{57} - 214 q^{58} - 160 q^{59} - 388 q^{60} - 352 q^{61} - 216 q^{62} - 138 q^{63} - 1264 q^{64} - 450 q^{65} - 420 q^{66} - 240 q^{67} - 750 q^{68} - 360 q^{69} - 642 q^{70} - 636 q^{71} - 572 q^{72} - 556 q^{73} - 662 q^{74} - 484 q^{75} - 626 q^{76} - 358 q^{77} - 728 q^{78} - 380 q^{79} - 666 q^{80} - 496 q^{81} - 564 q^{82} - 374 q^{83} - 616 q^{84} - 290 q^{85} - 296 q^{86} - 332 q^{87} - 24 q^{88} - 264 q^{89} - 564 q^{90} - 472 q^{91} - 264 q^{92} - 556 q^{93} - 70 q^{94} - 162 q^{95} - 688 q^{96} - 46 q^{97} - 356 q^{98} - 584 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1449))$$

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
1449.2.a $$\chi_{1449}(1, \cdot)$$ 1449.2.a.a 1 1
1449.2.a.b 1
1449.2.a.c 1
1449.2.a.d 1
1449.2.a.e 1
1449.2.a.f 2
1449.2.a.g 2
1449.2.a.h 2
1449.2.a.i 2
1449.2.a.j 2
1449.2.a.k 2
1449.2.a.l 3
1449.2.a.m 3
1449.2.a.n 4
1449.2.a.o 4
1449.2.a.p 4
1449.2.a.q 4
1449.2.a.r 5
1449.2.a.s 5
1449.2.a.t 5
1449.2.d $$\chi_{1449}(944, \cdot)$$ 1449.2.d.a 56 1
1449.2.e $$\chi_{1449}(827, \cdot)$$ 1449.2.e.a 48 1
1449.2.h $$\chi_{1449}(1126, \cdot)$$ 1449.2.h.a 2 1
1449.2.h.b 4
1449.2.h.c 4
1449.2.h.d 8
1449.2.h.e 12
1449.2.h.f 12
1449.2.h.g 12
1449.2.h.h 12
1449.2.h.i 12
1449.2.i $$\chi_{1449}(415, \cdot)$$ n/a 148 2
1449.2.j $$\chi_{1449}(484, \cdot)$$ n/a 264 2
1449.2.k $$\chi_{1449}(760, \cdot)$$ n/a 352 2
1449.2.l $$\chi_{1449}(277, \cdot)$$ n/a 352 2
1449.2.m $$\chi_{1449}(137, \cdot)$$ n/a 376 2
1449.2.n $$\chi_{1449}(668, \cdot)$$ n/a 352 2
1449.2.s $$\chi_{1449}(712, \cdot)$$ n/a 156 2
1449.2.t $$\chi_{1449}(160, \cdot)$$ n/a 376 2
1449.2.y $$\chi_{1449}(850, \cdot)$$ n/a 376 2
1449.2.bb $$\chi_{1449}(344, \cdot)$$ n/a 288 2
1449.2.bc $$\chi_{1449}(461, \cdot)$$ n/a 352 2
1449.2.bd $$\chi_{1449}(620, \cdot)$$ n/a 128 2
1449.2.be $$\chi_{1449}(530, \cdot)$$ n/a 120 2
1449.2.bj $$\chi_{1449}(47, \cdot)$$ n/a 352 2
1449.2.bk $$\chi_{1449}(758, \cdot)$$ n/a 376 2
1449.2.bl $$\chi_{1449}(229, \cdot)$$ n/a 376 2
1449.2.bo $$\chi_{1449}(64, \cdot)$$ n/a 600 10
1449.2.bp $$\chi_{1449}(181, \cdot)$$ n/a 780 10
1449.2.bs $$\chi_{1449}(134, \cdot)$$ n/a 480 10
1449.2.bt $$\chi_{1449}(62, \cdot)$$ n/a 640 10
1449.2.bw $$\chi_{1449}(25, \cdot)$$ n/a 3760 20
1449.2.bx $$\chi_{1449}(4, \cdot)$$ n/a 3760 20
1449.2.by $$\chi_{1449}(85, \cdot)$$ n/a 2880 20
1449.2.bz $$\chi_{1449}(100, \cdot)$$ n/a 1560 20
1449.2.cc $$\chi_{1449}(40, \cdot)$$ n/a 3760 20
1449.2.cd $$\chi_{1449}(65, \cdot)$$ n/a 3760 20
1449.2.ce $$\chi_{1449}(59, \cdot)$$ n/a 3760 20
1449.2.cj $$\chi_{1449}(26, \cdot)$$ n/a 1280 20
1449.2.ck $$\chi_{1449}(44, \cdot)$$ n/a 1280 20
1449.2.cl $$\chi_{1449}(41, \cdot)$$ n/a 3760 20
1449.2.cm $$\chi_{1449}(113, \cdot)$$ n/a 2880 20
1449.2.cp $$\chi_{1449}(61, \cdot)$$ n/a 3760 20
1449.2.cu $$\chi_{1449}(34, \cdot)$$ n/a 3760 20
1449.2.cv $$\chi_{1449}(10, \cdot)$$ n/a 1560 20
1449.2.da $$\chi_{1449}(101, \cdot)$$ n/a 3760 20
1449.2.db $$\chi_{1449}(11, \cdot)$$ n/a 3760 20

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1449))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1449)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(483))$$$$^{\oplus 2}$$