Properties

Label 550.6
Level 550
Weight 6
Dimension 13595
Nonzero newspaces 21
Sturm bound 108000
Trace bound 13

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Defining parameters

Level: \( N \) = \( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 21 \)
Sturm bound: \(108000\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(550))\).

Total New Old
Modular forms 45560 13595 31965
Cusp forms 44440 13595 30845
Eisenstein series 1120 0 1120

Trace form

\( 13595 q - 16 q^{2} + 16 q^{3} + 64 q^{4} + 170 q^{5} - 300 q^{6} - 1838 q^{7} - 256 q^{8} + 3712 q^{9} + O(q^{10}) \) \( 13595 q - 16 q^{2} + 16 q^{3} + 64 q^{4} + 170 q^{5} - 300 q^{6} - 1838 q^{7} - 256 q^{8} + 3712 q^{9} - 360 q^{10} - 590 q^{11} + 416 q^{12} - 554 q^{13} + 4072 q^{14} + 1640 q^{15} + 5120 q^{16} - 4768 q^{17} + 5452 q^{18} + 15035 q^{19} - 1280 q^{20} + 13060 q^{21} - 2816 q^{22} - 6604 q^{23} - 13504 q^{24} - 50670 q^{25} - 20240 q^{26} - 65135 q^{27} - 10848 q^{28} + 66700 q^{29} + 60000 q^{30} + 79030 q^{31} + 11264 q^{32} + 118831 q^{33} + 42712 q^{34} - 121720 q^{35} + 28880 q^{36} - 144438 q^{37} - 110360 q^{38} - 178006 q^{39} - 640 q^{40} + 34660 q^{41} - 276072 q^{42} + 85346 q^{43} + 102064 q^{44} + 278210 q^{45} + 406480 q^{46} + 529792 q^{47} + 4096 q^{48} - 95862 q^{49} - 51080 q^{50} - 425715 q^{51} - 286144 q^{52} - 768244 q^{53} - 945120 q^{54} - 391580 q^{55} - 61440 q^{56} - 161015 q^{57} - 84800 q^{58} + 100885 q^{59} - 98560 q^{60} + 627530 q^{61} + 794408 q^{62} + 2074496 q^{63} + 16384 q^{64} + 1243210 q^{65} + 371520 q^{66} + 753002 q^{67} - 27648 q^{68} - 647646 q^{69} - 761760 q^{70} - 234160 q^{71} - 209408 q^{72} - 836864 q^{73} - 1049168 q^{74} - 1784920 q^{75} - 121440 q^{76} - 850588 q^{77} + 137664 q^{78} - 668470 q^{79} + 43520 q^{80} + 891215 q^{81} + 859788 q^{82} + 765461 q^{83} + 243328 q^{84} + 1669010 q^{85} + 152660 q^{86} + 2336540 q^{87} + 10624 q^{88} + 557370 q^{89} - 488040 q^{90} - 1600980 q^{91} - 764704 q^{92} - 1170918 q^{93} - 179648 q^{94} - 85560 q^{95} - 81920 q^{96} + 1550807 q^{97} + 442788 q^{98} + 2952502 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(550))\)

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
550.6.a \(\chi_{550}(1, \cdot)\) 550.6.a.a 1 1
550.6.a.b 1
550.6.a.c 1
550.6.a.d 1
550.6.a.e 1
550.6.a.f 1
550.6.a.g 1
550.6.a.h 2
550.6.a.i 2
550.6.a.j 2
550.6.a.k 3
550.6.a.l 3
550.6.a.m 4
550.6.a.n 4
550.6.a.o 4
550.6.a.p 4
550.6.a.q 5
550.6.a.r 5
550.6.a.s 5
550.6.a.t 5
550.6.a.u 6
550.6.a.v 6
550.6.a.w 7
550.6.a.x 7
550.6.b \(\chi_{550}(199, \cdot)\) 550.6.b.a 2 1
550.6.b.b 2
550.6.b.c 2
550.6.b.d 2
550.6.b.e 2
550.6.b.f 2
550.6.b.g 2
550.6.b.h 4
550.6.b.i 4
550.6.b.j 4
550.6.b.k 6
550.6.b.l 6
550.6.b.m 8
550.6.b.n 8
550.6.b.o 10
550.6.b.p 10
550.6.f \(\chi_{550}(43, \cdot)\) n/a 180 2
550.6.g \(\chi_{550}(291, \cdot)\) n/a 600 4
550.6.h \(\chi_{550}(201, \cdot)\) n/a 380 4
550.6.i \(\chi_{550}(31, \cdot)\) n/a 600 4
550.6.j \(\chi_{550}(81, \cdot)\) n/a 600 4
550.6.k \(\chi_{550}(111, \cdot)\) n/a 496 4
550.6.l \(\chi_{550}(181, \cdot)\) n/a 600 4
550.6.n \(\chi_{550}(59, \cdot)\) n/a 600 4
550.6.t \(\chi_{550}(89, \cdot)\) n/a 504 4
550.6.y \(\chi_{550}(9, \cdot)\) n/a 600 4
550.6.z \(\chi_{550}(69, \cdot)\) n/a 600 4
550.6.ba \(\chi_{550}(49, \cdot)\) n/a 360 4
550.6.bb \(\chi_{550}(119, \cdot)\) n/a 600 4
550.6.be \(\chi_{550}(17, \cdot)\) n/a 1200 8
550.6.bh \(\chi_{550}(7, \cdot)\) n/a 720 8
550.6.bi \(\chi_{550}(87, \cdot)\) n/a 1200 8
550.6.bj \(\chi_{550}(13, \cdot)\) n/a 1200 8
550.6.bk \(\chi_{550}(123, \cdot)\) n/a 1200 8
550.6.bp \(\chi_{550}(63, \cdot)\) n/a 1200 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(550))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(550)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 2}\)