↑

Properties

Label 775.3
Level 775
Weight 3
Dimension 43553
Nonzero newspaces 42
Sturm bound 144000
Trace bound 7

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 42 \)
Sturm bound: \(144000\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(775))\).

Total New Old
Modular forms 48840 44743 4097
Cusp forms 47160 43553 3607
Eisenstein series 1680 1190 490

Trace form

\( 43553 q - 175 q^{2} - 175 q^{3} - 175 q^{4} - 220 q^{5} - 279 q^{6} - 175 q^{7} - 175 q^{8} - 175 q^{9} + O(q^{10}) \) \( 43553 q - 175 q^{2} - 175 q^{3} - 175 q^{4} - 220 q^{5} - 279 q^{6} - 175 q^{7} - 175 q^{8} - 175 q^{9} - 220 q^{10} - 279 q^{11} - 175 q^{12} - 175 q^{13} - 175 q^{14} - 220 q^{15} - 407 q^{16} - 315 q^{17} - 475 q^{18} - 375 q^{19} - 500 q^{20} - 354 q^{21} - 95 q^{22} - 110 q^{23} + 165 q^{24} - 160 q^{25} - 359 q^{26} + 140 q^{27} + 465 q^{28} + 55 q^{29} + 260 q^{30} - 187 q^{31} + 10 q^{32} + 95 q^{33} + 85 q^{34} - 727 q^{36} - 610 q^{37} - 1075 q^{38} - 1290 q^{39} - 1120 q^{40} - 764 q^{41} - 1935 q^{42} - 720 q^{43} - 875 q^{44} - 860 q^{45} - 639 q^{46} - 335 q^{47} + 70 q^{48} + 165 q^{49} - 40 q^{50} + 581 q^{51} + 1120 q^{52} + 425 q^{53} + 2280 q^{54} + 260 q^{55} + 980 q^{56} + 1465 q^{57} + 1400 q^{58} + 385 q^{59} + 860 q^{60} - 304 q^{61} - 345 q^{62} - 590 q^{63} - 1205 q^{64} - 960 q^{65} - 1788 q^{66} - 915 q^{67} - 2350 q^{68} - 1595 q^{69} - 860 q^{70} - 1119 q^{71} - 2730 q^{72} - 615 q^{73} - 1170 q^{74} - 60 q^{75} - 820 q^{76} + 500 q^{77} + 1300 q^{78} + 680 q^{79} + 1460 q^{80} + 293 q^{81} + 345 q^{82} + 750 q^{83} + 1265 q^{84} - 1440 q^{85} + 321 q^{86} - 495 q^{87} + 145 q^{88} + 50 q^{89} - 1000 q^{90} - 814 q^{91} - 120 q^{92} - 835 q^{93} - 2090 q^{94} - 860 q^{95} - 1734 q^{96} - 1060 q^{97} - 1615 q^{98} - 720 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(775))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
775.3.c \(\chi_{775}(774, \cdot)\) 775.3.c.a 4 1
775.3.c.b 6
775.3.c.c 8
775.3.c.d 32
775.3.c.e 44
775.3.d \(\chi_{775}(526, \cdot)\) 775.3.d.a 2 1
775.3.d.b 2
775.3.d.c 2
775.3.d.d 3
775.3.d.e 4
775.3.d.f 6
775.3.d.g 16
775.3.d.h 20
775.3.d.i 22
775.3.d.j 22
775.3.g \(\chi_{775}(32, \cdot)\) n/a 180 2
775.3.n \(\chi_{775}(99, \cdot)\) n/a 188 2
775.3.p \(\chi_{775}(26, \cdot)\) n/a 196 2
775.3.q \(\chi_{775}(339, \cdot)\) n/a 632 4
775.3.s \(\chi_{775}(246, \cdot)\) n/a 632 4
775.3.t \(\chi_{775}(151, \cdot)\) n/a 396 4
775.3.u \(\chi_{775}(91, \cdot)\) n/a 632 4
775.3.v \(\chi_{775}(46, \cdot)\) n/a 632 4
775.3.w \(\chi_{775}(61, \cdot)\) n/a 632 4
775.3.y \(\chi_{775}(399, \cdot)\) n/a 376 4
775.3.z \(\chi_{775}(154, \cdot)\) n/a 632 4
775.3.ba \(\chi_{775}(89, \cdot)\) n/a 632 4
775.3.bb \(\chi_{775}(54, \cdot)\) n/a 632 4
775.3.bg \(\chi_{775}(29, \cdot)\) n/a 632 4
775.3.bh \(\chi_{775}(581, \cdot)\) n/a 632 4
775.3.bi \(\chi_{775}(118, \cdot)\) n/a 376 4
775.3.bq \(\chi_{775}(2, \cdot)\) n/a 1264 8
775.3.bt \(\chi_{775}(233, \cdot)\) n/a 1264 8
775.3.bu \(\chi_{775}(33, \cdot)\) n/a 1264 8
775.3.bv \(\chi_{775}(63, \cdot)\) n/a 1200 8
775.3.bw \(\chi_{775}(188, \cdot)\) n/a 1264 8
775.3.cb \(\chi_{775}(132, \cdot)\) n/a 752 8
775.3.cd \(\chi_{775}(34, \cdot)\) n/a 1264 8
775.3.ce \(\chi_{775}(6, \cdot)\) n/a 1264 8
775.3.cf \(\chi_{775}(11, \cdot)\) n/a 1264 8
775.3.cg \(\chi_{775}(146, \cdot)\) n/a 1264 8
775.3.ch \(\chi_{775}(176, \cdot)\) n/a 784 8
775.3.ci \(\chi_{775}(21, \cdot)\) n/a 1264 8
775.3.cj \(\chi_{775}(44, \cdot)\) n/a 1264 8
775.3.co \(\chi_{775}(79, \cdot)\) n/a 1264 8
775.3.cp \(\chi_{775}(84, \cdot)\) n/a 1264 8
775.3.cq \(\chi_{775}(119, \cdot)\) n/a 1264 8
775.3.cr \(\chi_{775}(24, \cdot)\) n/a 752 8
775.3.ct \(\chi_{775}(136, \cdot)\) n/a 1264 8
775.3.cv \(\chi_{775}(133, \cdot)\) n/a 2528 16
775.3.cw \(\chi_{775}(7, \cdot)\) n/a 1504 16
775.3.db \(\chi_{775}(112, \cdot)\) n/a 2528 16
775.3.dc \(\chi_{775}(67, \cdot)\) n/a 2528 16
775.3.dd \(\chi_{775}(28, \cdot)\) n/a 2528 16
775.3.de \(\chi_{775}(38, \cdot)\) n/a 2528 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(775))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(775)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(775))\)\(^{\oplus 1}\)