# Properties

 Label 1225.2 Level 1225 Weight 2 Dimension 51010 Nonzero newspaces 24 Sturm bound 235200 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$1225 = 5^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$235200$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1225))$$.

Total New Old
Modular forms 60480 52999 7481
Cusp forms 57121 51010 6111
Eisenstein series 3359 1989 1370

## Trace form

 $$51010 q - 202 q^{2} - 199 q^{3} - 190 q^{4} - 245 q^{5} - 303 q^{6} - 230 q^{7} - 328 q^{8} - 172 q^{9} + O(q^{10})$$ $$51010 q - 202 q^{2} - 199 q^{3} - 190 q^{4} - 245 q^{5} - 303 q^{6} - 230 q^{7} - 328 q^{8} - 172 q^{9} - 235 q^{10} - 303 q^{11} - 127 q^{12} - 169 q^{13} - 216 q^{14} - 422 q^{15} - 262 q^{16} - 167 q^{17} - 119 q^{18} - 171 q^{19} - 250 q^{20} - 353 q^{21} - 305 q^{22} - 159 q^{23} - 293 q^{24} - 279 q^{25} - 639 q^{26} - 265 q^{27} - 284 q^{28} - 399 q^{29} - 374 q^{30} - 359 q^{31} - 345 q^{32} - 327 q^{33} - 314 q^{34} - 324 q^{35} - 818 q^{36} - 274 q^{37} - 295 q^{38} - 372 q^{39} - 369 q^{40} - 371 q^{41} - 381 q^{42} - 419 q^{43} - 347 q^{44} - 337 q^{45} - 405 q^{46} - 197 q^{47} - 452 q^{48} - 272 q^{49} - 793 q^{50} - 577 q^{51} - 373 q^{52} - 136 q^{53} - 395 q^{54} - 278 q^{55} - 498 q^{56} - 447 q^{57} - 479 q^{58} - 315 q^{59} - 490 q^{60} - 530 q^{61} - 507 q^{62} - 366 q^{63} - 750 q^{64} - 379 q^{65} - 591 q^{66} - 431 q^{67} - 577 q^{68} - 425 q^{69} - 468 q^{70} - 613 q^{71} - 612 q^{72} - 413 q^{73} - 507 q^{74} - 422 q^{75} - 917 q^{76} - 297 q^{77} - 683 q^{78} - 395 q^{79} - 547 q^{80} - 424 q^{81} - 538 q^{82} - 345 q^{83} - 608 q^{84} - 563 q^{85} - 498 q^{86} - 389 q^{87} - 774 q^{88} - 390 q^{89} - 601 q^{90} - 463 q^{91} - 732 q^{92} - 545 q^{93} - 512 q^{94} - 422 q^{95} - 874 q^{96} - 450 q^{97} - 672 q^{98} - 860 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1225))$$

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
1225.2.a $$\chi_{1225}(1, \cdot)$$ 1225.2.a.a 1 1
1225.2.a.b 1
1225.2.a.c 1
1225.2.a.d 1
1225.2.a.e 1
1225.2.a.f 1
1225.2.a.g 1
1225.2.a.h 1
1225.2.a.i 1
1225.2.a.j 1
1225.2.a.k 2
1225.2.a.l 2
1225.2.a.m 2
1225.2.a.n 2
1225.2.a.o 2
1225.2.a.p 2
1225.2.a.q 2
1225.2.a.r 2
1225.2.a.s 2
1225.2.a.t 2
1225.2.a.u 2
1225.2.a.v 2
1225.2.a.w 3
1225.2.a.x 3
1225.2.a.y 3
1225.2.a.z 3
1225.2.a.ba 4
1225.2.a.bb 4
1225.2.a.bc 4
1225.2.b $$\chi_{1225}(99, \cdot)$$ 1225.2.b.a 2 1
1225.2.b.b 2
1225.2.b.c 2
1225.2.b.d 2
1225.2.b.e 4
1225.2.b.f 4
1225.2.b.g 4
1225.2.b.h 4
1225.2.b.i 4
1225.2.b.j 4
1225.2.b.k 4
1225.2.b.l 6
1225.2.b.m 6
1225.2.b.n 8
1225.2.e $$\chi_{1225}(226, \cdot)$$ n/a 114 2
1225.2.f $$\chi_{1225}(293, \cdot)$$ n/a 112 2
1225.2.h $$\chi_{1225}(246, \cdot)$$ n/a 388 4
1225.2.k $$\chi_{1225}(324, \cdot)$$ n/a 112 2
1225.2.l $$\chi_{1225}(176, \cdot)$$ n/a 510 6
1225.2.o $$\chi_{1225}(344, \cdot)$$ n/a 392 4
1225.2.p $$\chi_{1225}(68, \cdot)$$ n/a 224 4
1225.2.t $$\chi_{1225}(274, \cdot)$$ n/a 492 6
1225.2.u $$\chi_{1225}(116, \cdot)$$ n/a 768 8
1225.2.w $$\chi_{1225}(48, \cdot)$$ n/a 768 8
1225.2.x $$\chi_{1225}(51, \cdot)$$ n/a 1032 12
1225.2.z $$\chi_{1225}(118, \cdot)$$ n/a 984 12
1225.2.ba $$\chi_{1225}(79, \cdot)$$ n/a 768 8
1225.2.bd $$\chi_{1225}(36, \cdot)$$ n/a 3312 24
1225.2.be $$\chi_{1225}(74, \cdot)$$ n/a 984 12
1225.2.bi $$\chi_{1225}(117, \cdot)$$ n/a 1536 16
1225.2.bj $$\chi_{1225}(29, \cdot)$$ n/a 3312 24
1225.2.bn $$\chi_{1225}(82, \cdot)$$ n/a 1968 24
1225.2.bo $$\chi_{1225}(11, \cdot)$$ n/a 6624 48
1225.2.bp $$\chi_{1225}(13, \cdot)$$ n/a 6624 48
1225.2.bt $$\chi_{1225}(4, \cdot)$$ n/a 6624 48
1225.2.bu $$\chi_{1225}(3, \cdot)$$ n/a 13248 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1225))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1225)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1225))$$$$^{\oplus 1}$$