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Properties

Label 800.6
Level 800
Weight 6
Dimension 49565
Nonzero newspaces 20
Sturm bound 230400
Trace bound 7

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Defining parameters

Level: \( N \) = \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(230400\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(800))\).

Total New Old
Modular forms 96896 49975 46921
Cusp forms 95104 49565 45539
Eisenstein series 1792 410 1382

Trace form

\( 49565 q - 52 q^{2} - 40 q^{3} - 52 q^{4} - 64 q^{5} - 84 q^{6} - 136 q^{7} - 52 q^{8} + 209 q^{9} + O(q^{10}) \) \( 49565 q - 52 q^{2} - 40 q^{3} - 52 q^{4} - 64 q^{5} - 84 q^{6} - 136 q^{7} - 52 q^{8} + 209 q^{9} - 64 q^{10} - 64 q^{11} - 1636 q^{12} + 58 q^{13} + 2428 q^{14} - 48 q^{15} + 4096 q^{16} + 1786 q^{17} - 1672 q^{18} - 32 q^{19} - 64 q^{20} - 5972 q^{21} - 12432 q^{22} - 704 q^{23} + 21408 q^{24} - 96 q^{25} + 12816 q^{26} - 5560 q^{27} - 2232 q^{28} + 37882 q^{29} - 64 q^{30} + 7284 q^{31} - 18632 q^{32} - 64752 q^{33} - 6304 q^{34} - 4824 q^{35} + 65504 q^{36} + 67970 q^{37} + 356 q^{38} + 17288 q^{39} - 64 q^{40} + 41662 q^{41} - 53672 q^{42} + 34656 q^{43} + 3668 q^{44} - 61624 q^{45} + 63244 q^{46} - 75828 q^{47} + 112320 q^{48} - 79543 q^{49} - 64 q^{50} + 21728 q^{51} + 18420 q^{52} + 34978 q^{53} + 1264 q^{54} + 12452 q^{55} - 81064 q^{56} - 138988 q^{57} - 84624 q^{58} - 28992 q^{59} - 16448 q^{60} + 204586 q^{61} + 63432 q^{62} - 137876 q^{63} - 1155256 q^{64} - 141632 q^{65} - 5572 q^{66} + 117312 q^{67} + 1062592 q^{68} + 869036 q^{69} + 798992 q^{70} + 224768 q^{71} + 1466564 q^{72} + 80734 q^{73} + 19100 q^{74} - 127784 q^{75} - 718244 q^{76} - 783652 q^{77} - 3473948 q^{78} - 251484 q^{79} - 985824 q^{80} - 1135207 q^{81} - 1033972 q^{82} - 582160 q^{83} - 242224 q^{84} + 63200 q^{85} + 998128 q^{86} - 23784 q^{87} + 2291920 q^{88} + 864302 q^{89} + 2382896 q^{90} + 858928 q^{91} + 2119896 q^{92} + 1614400 q^{93} + 631896 q^{94} - 25972 q^{95} - 2934736 q^{96} - 1026526 q^{97} - 3639608 q^{98} + 338496 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(800))\)

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
800.6.a \(\chi_{800}(1, \cdot)\) 800.6.a.a 1 1
800.6.a.b 1
800.6.a.c 1
800.6.a.d 1
800.6.a.e 1
800.6.a.f 2
800.6.a.g 2
800.6.a.h 2
800.6.a.i 2
800.6.a.j 2
800.6.a.k 2
800.6.a.l 2
800.6.a.m 2
800.6.a.n 3
800.6.a.o 3
800.6.a.p 4
800.6.a.q 4
800.6.a.r 4
800.6.a.s 5
800.6.a.t 5
800.6.a.u 5
800.6.a.v 5
800.6.a.w 6
800.6.a.x 6
800.6.a.y 6
800.6.a.z 6
800.6.a.ba 6
800.6.a.bb 6
800.6.c \(\chi_{800}(449, \cdot)\) 800.6.c.a 2 1
800.6.c.b 2
800.6.c.c 2
800.6.c.d 4
800.6.c.e 4
800.6.c.f 4
800.6.c.g 4
800.6.c.h 4
800.6.c.i 4
800.6.c.j 6
800.6.c.k 6
800.6.c.l 8
800.6.c.m 8
800.6.c.n 10
800.6.c.o 10
800.6.c.p 12
800.6.d \(\chi_{800}(401, \cdot)\) 800.6.d.a 4 1
800.6.d.b 20
800.6.d.c 20
800.6.d.d 20
800.6.d.e 28
800.6.f \(\chi_{800}(49, \cdot)\) 800.6.f.a 8 1
800.6.f.b 20
800.6.f.c 20
800.6.f.d 40
800.6.j \(\chi_{800}(407, \cdot)\) None 0 2
800.6.l \(\chi_{800}(201, \cdot)\) None 0 2
800.6.n \(\chi_{800}(543, \cdot)\) n/a 180 2
800.6.o \(\chi_{800}(143, \cdot)\) n/a 176 2
800.6.q \(\chi_{800}(249, \cdot)\) None 0 2
800.6.s \(\chi_{800}(7, \cdot)\) None 0 2
800.6.u \(\chi_{800}(161, \cdot)\) n/a 600 4
800.6.v \(\chi_{800}(43, \cdot)\) n/a 1432 4
800.6.y \(\chi_{800}(101, \cdot)\) n/a 1508 4
800.6.ba \(\chi_{800}(149, \cdot)\) n/a 1432 4
800.6.bb \(\chi_{800}(107, \cdot)\) n/a 1432 4
800.6.be \(\chi_{800}(209, \cdot)\) n/a 592 4
800.6.bg \(\chi_{800}(129, \cdot)\) n/a 600 4
800.6.bj \(\chi_{800}(81, \cdot)\) n/a 592 4
800.6.bl \(\chi_{800}(23, \cdot)\) None 0 8
800.6.bm \(\chi_{800}(41, \cdot)\) None 0 8
800.6.bp \(\chi_{800}(47, \cdot)\) n/a 1184 8
800.6.bq \(\chi_{800}(63, \cdot)\) n/a 1200 8
800.6.bt \(\chi_{800}(9, \cdot)\) None 0 8
800.6.bu \(\chi_{800}(87, \cdot)\) None 0 8
800.6.bx \(\chi_{800}(67, \cdot)\) n/a 9568 16
800.6.by \(\chi_{800}(29, \cdot)\) n/a 9568 16
800.6.ca \(\chi_{800}(21, \cdot)\) n/a 9568 16
800.6.cd \(\chi_{800}(3, \cdot)\) n/a 9568 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(800))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(800)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)