## Defining parameters

 Level: $$N$$ = $$1450 = 2 \cdot 5^{2} \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$252000$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1450))$$.

Total New Old
Modular forms 64568 19307 45261
Cusp forms 61433 19307 42126
Eisenstein series 3135 0 3135

## Trace form

 $$19307 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + O(q^{10})$$ $$19307 q + 2 q^{2} + 8 q^{3} + 2 q^{4} + 10 q^{5} + 8 q^{6} + 16 q^{7} + 2 q^{8} + 26 q^{9} + 10 q^{10} + 24 q^{11} + 8 q^{12} + 28 q^{13} + 16 q^{14} + 40 q^{15} + 2 q^{16} - 4 q^{17} - 24 q^{18} - 40 q^{19} + 40 q^{21} - 28 q^{22} - 4 q^{23} - 4 q^{24} - 70 q^{25} + 23 q^{26} + 44 q^{27} - 24 q^{28} + 46 q^{29} - 40 q^{30} + 40 q^{31} - 8 q^{32} + 100 q^{33} + 21 q^{34} + 40 q^{35} + 54 q^{36} + 94 q^{37} + 68 q^{38} + 88 q^{39} + 10 q^{40} + 44 q^{41} + 64 q^{42} + 8 q^{43} + 24 q^{44} - 30 q^{45} + 48 q^{46} + 44 q^{47} + 8 q^{48} + 80 q^{49} + 50 q^{50} + 80 q^{51} + 28 q^{52} + 81 q^{53} + 80 q^{54} + 40 q^{55} + 16 q^{56} + 56 q^{57} + 30 q^{58} + 28 q^{59} + 60 q^{61} - 56 q^{62} + 40 q^{63} + 2 q^{64} - 70 q^{65} - 24 q^{66} + 32 q^{67} - 84 q^{68} - 32 q^{69} - 80 q^{70} + 96 q^{71} + 26 q^{72} + 79 q^{73} - 40 q^{74} - 120 q^{75} + 16 q^{76} + 12 q^{77} + 24 q^{78} + 56 q^{79} + 10 q^{80} + 306 q^{81} - 20 q^{82} - 40 q^{83} + 28 q^{84} - 30 q^{85} + 108 q^{86} + 120 q^{87} + 24 q^{88} + 110 q^{89} + 10 q^{90} + 232 q^{91} + 92 q^{92} + 248 q^{93} + 152 q^{94} + 120 q^{95} + 8 q^{96} + 219 q^{97} + 226 q^{98} + 388 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1450))$$

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
1450.2.a $$\chi_{1450}(1, \cdot)$$ 1450.2.a.a 1 1
1450.2.a.b 1
1450.2.a.c 1
1450.2.a.d 1
1450.2.a.e 1
1450.2.a.f 1
1450.2.a.g 1
1450.2.a.h 1
1450.2.a.i 1
1450.2.a.j 2
1450.2.a.k 2
1450.2.a.l 2
1450.2.a.m 2
1450.2.a.n 2
1450.2.a.o 2
1450.2.a.p 3
1450.2.a.q 3
1450.2.a.r 3
1450.2.a.s 3
1450.2.a.t 5
1450.2.a.u 5
1450.2.b $$\chi_{1450}(349, \cdot)$$ 1450.2.b.a 2 1
1450.2.b.b 2
1450.2.b.c 2
1450.2.b.d 2
1450.2.b.e 2
1450.2.b.f 2
1450.2.b.g 4
1450.2.b.h 4
1450.2.b.i 4
1450.2.b.j 6
1450.2.b.k 6
1450.2.b.l 6
1450.2.c $$\chi_{1450}(1101, \cdot)$$ 1450.2.c.a 2 1
1450.2.c.b 2
1450.2.c.c 4
1450.2.c.d 4
1450.2.c.e 10
1450.2.c.f 10
1450.2.c.g 16
1450.2.d $$\chi_{1450}(1449, \cdot)$$ 1450.2.d.a 2 1
1450.2.d.b 2
1450.2.d.c 2
1450.2.d.d 2
1450.2.d.e 4
1450.2.d.f 4
1450.2.d.g 4
1450.2.d.h 4
1450.2.d.i 10
1450.2.d.j 10
1450.2.e $$\chi_{1450}(307, \cdot)$$ 1450.2.e.a 2 2
1450.2.e.b 2
1450.2.e.c 2
1450.2.e.d 4
1450.2.e.e 8
1450.2.e.f 10
1450.2.e.g 10
1450.2.e.h 12
1450.2.e.i 20
1450.2.e.j 20
1450.2.j $$\chi_{1450}(157, \cdot)$$ 1450.2.j.a 2 2
1450.2.j.b 2
1450.2.j.c 2
1450.2.j.d 4
1450.2.j.e 8
1450.2.j.f 10
1450.2.j.g 10
1450.2.j.h 12
1450.2.j.i 20
1450.2.j.j 20
1450.2.k $$\chi_{1450}(291, \cdot)$$ n/a 280 4
1450.2.l $$\chi_{1450}(401, \cdot)$$ n/a 282 6
1450.2.m $$\chi_{1450}(289, \cdot)$$ n/a 304 4
1450.2.n $$\chi_{1450}(59, \cdot)$$ n/a 280 4
1450.2.o $$\chi_{1450}(231, \cdot)$$ n/a 296 4
1450.2.p $$\chi_{1450}(149, \cdot)$$ n/a 264 6
1450.2.q $$\chi_{1450}(51, \cdot)$$ n/a 288 6
1450.2.r $$\chi_{1450}(49, \cdot)$$ n/a 276 6
1450.2.s $$\chi_{1450}(133, \cdot)$$ n/a 600 8
1450.2.x $$\chi_{1450}(17, \cdot)$$ n/a 600 8
1450.2.y $$\chi_{1450}(43, \cdot)$$ n/a 540 12
1450.2.bd $$\chi_{1450}(143, \cdot)$$ n/a 540 12
1450.2.be $$\chi_{1450}(81, \cdot)$$ n/a 1824 24
1450.2.bf $$\chi_{1450}(71, \cdot)$$ n/a 1776 24
1450.2.bg $$\chi_{1450}(139, \cdot)$$ n/a 1776 24
1450.2.bh $$\chi_{1450}(9, \cdot)$$ n/a 1824 24
1450.2.bi $$\chi_{1450}(73, \cdot)$$ n/a 3600 48
1450.2.bn $$\chi_{1450}(3, \cdot)$$ n/a 3600 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1450))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1450)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(145))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(290))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(725))$$$$^{\oplus 2}$$