Properties

 Label 225.2 Level 225 Weight 2 Dimension 1221 Nonzero newspaces 12 Newforms 34 Sturm bound 7200 Trace bound 2

Defining parameters

 Level: $$N$$ = $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newforms: $$34$$ Sturm bound: $$7200$$ Trace bound: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(225))$$.

Total New Old
Modular forms 2024 1406 618
Cusp forms 1577 1221 356
Eisenstein series 447 185 262

Trace form

 $$1221q$$ $$\mathstrut -\mathstrut 16q^{2}$$ $$\mathstrut -\mathstrut 24q^{3}$$ $$\mathstrut -\mathstrut 8q^{4}$$ $$\mathstrut -\mathstrut 21q^{5}$$ $$\mathstrut -\mathstrut 40q^{6}$$ $$\mathstrut -\mathstrut 6q^{7}$$ $$\mathstrut -\mathstrut 24q^{8}$$ $$\mathstrut -\mathstrut 32q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$1221q$$ $$\mathstrut -\mathstrut 16q^{2}$$ $$\mathstrut -\mathstrut 24q^{3}$$ $$\mathstrut -\mathstrut 8q^{4}$$ $$\mathstrut -\mathstrut 21q^{5}$$ $$\mathstrut -\mathstrut 40q^{6}$$ $$\mathstrut -\mathstrut 6q^{7}$$ $$\mathstrut -\mathstrut 24q^{8}$$ $$\mathstrut -\mathstrut 32q^{9}$$ $$\mathstrut -\mathstrut 75q^{10}$$ $$\mathstrut -\mathstrut 46q^{11}$$ $$\mathstrut -\mathstrut 56q^{12}$$ $$\mathstrut -\mathstrut 26q^{13}$$ $$\mathstrut -\mathstrut 54q^{14}$$ $$\mathstrut -\mathstrut 44q^{15}$$ $$\mathstrut -\mathstrut 56q^{16}$$ $$\mathstrut -\mathstrut 44q^{17}$$ $$\mathstrut -\mathstrut 72q^{18}$$ $$\mathstrut -\mathstrut 70q^{19}$$ $$\mathstrut -\mathstrut 90q^{20}$$ $$\mathstrut -\mathstrut 72q^{21}$$ $$\mathstrut -\mathstrut 86q^{22}$$ $$\mathstrut -\mathstrut 74q^{23}$$ $$\mathstrut -\mathstrut 112q^{24}$$ $$\mathstrut -\mathstrut 63q^{25}$$ $$\mathstrut -\mathstrut 132q^{26}$$ $$\mathstrut -\mathstrut 72q^{27}$$ $$\mathstrut -\mathstrut 166q^{28}$$ $$\mathstrut -\mathstrut 94q^{29}$$ $$\mathstrut -\mathstrut 72q^{30}$$ $$\mathstrut -\mathstrut 58q^{31}$$ $$\mathstrut -\mathstrut 91q^{32}$$ $$\mathstrut -\mathstrut 56q^{33}$$ $$\mathstrut -\mathstrut 83q^{34}$$ $$\mathstrut -\mathstrut 32q^{35}$$ $$\mathstrut -\mathstrut 8q^{36}$$ $$\mathstrut -\mathstrut 99q^{37}$$ $$\mathstrut -\mathstrut 28q^{38}$$ $$\mathstrut +\mathstrut 24q^{39}$$ $$\mathstrut -\mathstrut 57q^{40}$$ $$\mathstrut +\mathstrut 26q^{41}$$ $$\mathstrut +\mathstrut 32q^{42}$$ $$\mathstrut -\mathstrut 6q^{43}$$ $$\mathstrut +\mathstrut 36q^{44}$$ $$\mathstrut -\mathstrut 12q^{45}$$ $$\mathstrut -\mathstrut 142q^{46}$$ $$\mathstrut +\mathstrut 10q^{47}$$ $$\mathstrut +\mathstrut 80q^{48}$$ $$\mathstrut -\mathstrut 91q^{49}$$ $$\mathstrut -\mathstrut 89q^{50}$$ $$\mathstrut -\mathstrut 80q^{51}$$ $$\mathstrut -\mathstrut 144q^{52}$$ $$\mathstrut -\mathstrut 79q^{53}$$ $$\mathstrut -\mathstrut 32q^{54}$$ $$\mathstrut -\mathstrut 142q^{55}$$ $$\mathstrut -\mathstrut 66q^{56}$$ $$\mathstrut -\mathstrut 72q^{57}$$ $$\mathstrut -\mathstrut 152q^{58}$$ $$\mathstrut -\mathstrut 128q^{59}$$ $$\mathstrut +\mathstrut 20q^{60}$$ $$\mathstrut -\mathstrut 66q^{61}$$ $$\mathstrut -\mathstrut 68q^{62}$$ $$\mathstrut -\mathstrut 60q^{63}$$ $$\mathstrut +\mathstrut 22q^{64}$$ $$\mathstrut +\mathstrut 53q^{65}$$ $$\mathstrut -\mathstrut 128q^{66}$$ $$\mathstrut +\mathstrut 42q^{67}$$ $$\mathstrut +\mathstrut 190q^{68}$$ $$\mathstrut -\mathstrut 20q^{69}$$ $$\mathstrut +\mathstrut 150q^{70}$$ $$\mathstrut -\mathstrut 62q^{71}$$ $$\mathstrut +\mathstrut 192q^{72}$$ $$\mathstrut +\mathstrut 34q^{73}$$ $$\mathstrut +\mathstrut 304q^{74}$$ $$\mathstrut +\mathstrut 128q^{75}$$ $$\mathstrut +\mathstrut 52q^{76}$$ $$\mathstrut +\mathstrut 234q^{77}$$ $$\mathstrut +\mathstrut 240q^{78}$$ $$\mathstrut +\mathstrut 114q^{79}$$ $$\mathstrut +\mathstrut 425q^{80}$$ $$\mathstrut +\mathstrut 88q^{81}$$ $$\mathstrut +\mathstrut 170q^{82}$$ $$\mathstrut +\mathstrut 284q^{83}$$ $$\mathstrut +\mathstrut 344q^{84}$$ $$\mathstrut +\mathstrut 21q^{85}$$ $$\mathstrut +\mathstrut 266q^{86}$$ $$\mathstrut +\mathstrut 148q^{87}$$ $$\mathstrut +\mathstrut 90q^{88}$$ $$\mathstrut +\mathstrut 177q^{89}$$ $$\mathstrut +\mathstrut 184q^{90}$$ $$\mathstrut -\mathstrut 86q^{91}$$ $$\mathstrut +\mathstrut 182q^{92}$$ $$\mathstrut +\mathstrut 100q^{93}$$ $$\mathstrut -\mathstrut 182q^{94}$$ $$\mathstrut -\mathstrut 70q^{95}$$ $$\mathstrut +\mathstrut 136q^{96}$$ $$\mathstrut -\mathstrut 174q^{97}$$ $$\mathstrut +\mathstrut 56q^{98}$$ $$\mathstrut +\mathstrut O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$

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
225.2.a $$\chi_{225}(1, \cdot)$$ 225.2.a.a 1 1
225.2.a.b 1
225.2.a.c 1
225.2.a.d 1
225.2.a.e 1
225.2.a.f 2
225.2.b $$\chi_{225}(199, \cdot)$$ 225.2.b.a 2 1
225.2.b.b 2
225.2.b.c 2
225.2.e $$\chi_{225}(76, \cdot)$$ 225.2.e.a 2 2
225.2.e.b 6
225.2.e.c 8
225.2.e.d 8
225.2.e.e 8
225.2.f $$\chi_{225}(107, \cdot)$$ 225.2.f.a 4 2
225.2.f.b 8
225.2.h $$\chi_{225}(46, \cdot)$$ 225.2.h.a 4 4
225.2.h.b 4
225.2.h.c 8
225.2.h.d 12
225.2.h.e 16
225.2.k $$\chi_{225}(49, \cdot)$$ 225.2.k.a 4 2
225.2.k.b 12
225.2.k.c 16
225.2.m $$\chi_{225}(19, \cdot)$$ 225.2.m.a 8 4
225.2.m.b 16
225.2.m.c 24
225.2.p $$\chi_{225}(32, \cdot)$$ 225.2.p.a 16 4
225.2.p.b 16
225.2.p.c 32
225.2.q $$\chi_{225}(16, \cdot)$$ 225.2.q.a 224 8
225.2.s $$\chi_{225}(8, \cdot)$$ 225.2.s.a 80 8
225.2.u $$\chi_{225}(4, \cdot)$$ 225.2.u.a 224 8
225.2.w $$\chi_{225}(2, \cdot)$$ 225.2.w.a 448 16

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(225))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(225)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 2}$$