# Properties

 Label 150.11 Level 150 Weight 11 Dimension 1384 Nonzero newspaces 6 Sturm bound 13200 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ = $$11$$ Nonzero newspaces: $$6$$ Sturm bound: $$13200$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{11}(\Gamma_1(150))$$.

Total New Old
Modular forms 6112 1384 4728
Cusp forms 5888 1384 4504
Eisenstein series 224 0 224

## Trace form

 $$1384 q - 128 q^{2} - 164 q^{3} - 2048 q^{4} + 15120 q^{5} - 18944 q^{6} - 2696 q^{7} + 65536 q^{8} - 76588 q^{9} + O(q^{10})$$ $$1384 q - 128 q^{2} - 164 q^{3} - 2048 q^{4} + 15120 q^{5} - 18944 q^{6} - 2696 q^{7} + 65536 q^{8} - 76588 q^{9} - 15168 q^{10} + 64160 q^{11} + 83968 q^{12} - 404544 q^{13} - 927724 q^{15} - 9437184 q^{16} - 7518768 q^{17} + 8796224 q^{18} - 7363528 q^{19} - 6381568 q^{20} - 14245232 q^{21} + 52952064 q^{22} + 34344592 q^{23} - 2752512 q^{24} - 122885916 q^{25} - 23767040 q^{26} + 38142412 q^{27} + 95547392 q^{28} + 341738000 q^{29} + 111494400 q^{30} - 142552488 q^{31} - 50331648 q^{32} - 136180008 q^{33} + 361024704 q^{34} + 615188552 q^{35} - 230037504 q^{36} + 353469864 q^{37} - 70408192 q^{38} - 800994360 q^{39} - 7766016 q^{40} - 38457920 q^{41} + 1015524352 q^{42} + 671203608 q^{43} - 333178420 q^{45} - 2340529664 q^{46} + 2948115808 q^{47} - 42991616 q^{48} + 3569619180 q^{49} - 817307072 q^{50} + 366697112 q^{51} - 1369694208 q^{52} - 4720140560 q^{53} - 3333031680 q^{54} + 3169133456 q^{55} + 836239360 q^{56} + 11589353752 q^{57} + 5825249792 q^{58} - 7071044000 q^{59} + 2530906112 q^{60} - 7449262904 q^{61} - 8910640640 q^{62} - 10623612668 q^{63} - 536870912 q^{64} - 3262614676 q^{65} + 13027483648 q^{66} + 3256555000 q^{67} - 4885172224 q^{68} - 531028212 q^{69} + 1083802368 q^{70} - 6651107840 q^{71} - 3858694144 q^{72} - 11117681584 q^{73} + 27225287324 q^{75} + 6996586496 q^{76} + 4237285696 q^{77} + 32579798528 q^{78} - 20655513432 q^{79} - 3963617280 q^{80} - 15396840052 q^{81} - 17732642816 q^{82} - 23547089024 q^{83} - 8135018496 q^{84} + 47272024104 q^{85} + 31824983040 q^{86} + 103863029356 q^{87} + 11477450752 q^{88} - 4481679500 q^{89} - 29399608896 q^{90} - 103684272400 q^{91} - 30207328256 q^{92} + 10075413340 q^{93} - 34523975680 q^{94} + 6269022016 q^{95} - 4966055936 q^{96} + 177534779680 q^{97} + 99105795968 q^{98} + 144198526688 q^{99} + O(q^{100})$$

## Decomposition of $$S_{11}^{\mathrm{new}}(\Gamma_1(150))$$

We only show spaces with odd 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
150.11.b $$\chi_{150}(149, \cdot)$$ 150.11.b.a 8 1
150.11.b.b 24
150.11.b.c 28
150.11.d $$\chi_{150}(101, \cdot)$$ 150.11.d.a 4 1
150.11.d.b 12
150.11.d.c 14
150.11.d.d 14
150.11.d.e 20
150.11.f $$\chi_{150}(7, \cdot)$$ 150.11.f.a 4 2
150.11.f.b 4
150.11.f.c 8
150.11.f.d 8
150.11.f.e 8
150.11.f.f 8
150.11.f.g 8
150.11.f.h 12
150.11.i $$\chi_{150}(29, \cdot)$$ n/a 400 4
150.11.j $$\chi_{150}(11, \cdot)$$ n/a 400 4
150.11.k $$\chi_{150}(13, \cdot)$$ n/a 400 8

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

## Decomposition of $$S_{11}^{\mathrm{old}}(\Gamma_1(150))$$ into lower level spaces

$$S_{11}^{\mathrm{old}}(\Gamma_1(150)) \cong$$ $$S_{11}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 3}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 4}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 2}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 2}$$$$\oplus$$$$S_{11}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 2}$$