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Properties

Label 3775.2
Level 3775
Weight 2
Dimension 522251
Nonzero newspaces 72
Sturm bound 2280000
Trace bound 12

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Defining parameters

Level: \( N \) = \( 3775 = 5^{2} \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(2280000\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3775))\).

Total New Old
Modular forms 574200 528359 45841
Cusp forms 565801 522251 43550
Eisenstein series 8399 6108 2291

Trace form

\( 522251 q - 961 q^{2} - 963 q^{3} - 969 q^{4} - 1190 q^{5} - 1563 q^{6} - 971 q^{7} - 985 q^{8} - 981 q^{9} + O(q^{10}) \) \( 522251 q - 961 q^{2} - 963 q^{3} - 969 q^{4} - 1190 q^{5} - 1563 q^{6} - 971 q^{7} - 985 q^{8} - 981 q^{9} - 1210 q^{10} - 1563 q^{11} - 1011 q^{12} - 983 q^{13} - 1003 q^{14} - 1220 q^{15} - 1569 q^{16} - 971 q^{17} - 983 q^{18} - 955 q^{19} - 1180 q^{20} - 1563 q^{21} - 947 q^{22} - 963 q^{23} - 935 q^{24} - 1170 q^{25} - 3063 q^{26} - 975 q^{27} - 947 q^{28} - 975 q^{29} - 1220 q^{30} - 1563 q^{31} - 1011 q^{32} - 1011 q^{33} - 1013 q^{34} - 1240 q^{35} - 1609 q^{36} - 1021 q^{37} - 1015 q^{38} - 987 q^{39} - 1230 q^{40} - 1583 q^{41} - 947 q^{42} - 963 q^{43} - 983 q^{44} - 1150 q^{45} - 1563 q^{46} - 971 q^{47} - 903 q^{48} - 959 q^{49} - 1150 q^{50} - 3043 q^{51} - 931 q^{52} - 973 q^{53} - 935 q^{54} - 1220 q^{55} - 1595 q^{56} - 955 q^{57} - 995 q^{58} - 975 q^{59} - 1180 q^{60} - 1583 q^{61} - 927 q^{62} - 983 q^{63} - 989 q^{64} - 1210 q^{65} - 1611 q^{66} - 1011 q^{67} - 967 q^{68} - 1007 q^{69} - 1260 q^{70} - 1603 q^{71} - 1005 q^{72} - 1023 q^{73} - 963 q^{74} - 1220 q^{75} - 3075 q^{76} - 987 q^{77} - 1031 q^{78} - 1035 q^{79} - 1210 q^{80} - 1629 q^{81} - 967 q^{82} - 903 q^{83} - 1003 q^{84} - 1130 q^{85} - 1563 q^{86} - 935 q^{87} - 915 q^{88} - 885 q^{89} - 1150 q^{90} - 1563 q^{91} - 1011 q^{92} - 951 q^{93} - 923 q^{94} - 1220 q^{95} - 1603 q^{96} - 871 q^{97} - 977 q^{98} - 1007 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3775))\)

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
3775.2.a \(\chi_{3775}(1, \cdot)\) 3775.2.a.a 1 1
3775.2.a.b 1
3775.2.a.c 1
3775.2.a.d 1
3775.2.a.e 1
3775.2.a.f 1
3775.2.a.g 2
3775.2.a.h 2
3775.2.a.i 2
3775.2.a.j 3
3775.2.a.k 3
3775.2.a.l 4
3775.2.a.m 4
3775.2.a.n 5
3775.2.a.o 5
3775.2.a.p 6
3775.2.a.q 15
3775.2.a.r 18
3775.2.a.s 22
3775.2.a.t 23
3775.2.a.u 23
3775.2.a.v 25
3775.2.a.w 25
3775.2.a.x 44
3775.2.b \(\chi_{3775}(3474, \cdot)\) n/a 226 1
3775.2.e \(\chi_{3775}(1326, \cdot)\) n/a 476 2
3775.2.f \(\chi_{3775}(1207, \cdot)\) n/a 452 2
3775.2.h \(\chi_{3775}(361, \cdot)\) n/a 1512 4
3775.2.i \(\chi_{3775}(321, \cdot)\) n/a 1512 4
3775.2.j \(\chi_{3775}(756, \cdot)\) n/a 1504 4
3775.2.k \(\chi_{3775}(1216, \cdot)\) n/a 1512 4
3775.2.l \(\chi_{3775}(461, \cdot)\) n/a 1512 4
3775.2.m \(\chi_{3775}(1076, \cdot)\) n/a 948 4
3775.2.o \(\chi_{3775}(1024, \cdot)\) n/a 452 2
3775.2.r \(\chi_{3775}(774, \cdot)\) n/a 904 4
3775.2.x \(\chi_{3775}(914, \cdot)\) n/a 1512 4
3775.2.bc \(\chi_{3775}(454, \cdot)\) n/a 1496 4
3775.2.bd \(\chi_{3775}(19, \cdot)\) n/a 1512 4
3775.2.be \(\chi_{3775}(59, \cdot)\) n/a 1512 4
3775.2.bf \(\chi_{3775}(159, \cdot)\) n/a 1512 4
3775.2.bj \(\chi_{3775}(1543, \cdot)\) n/a 904 4
3775.2.bk \(\chi_{3775}(76, \cdot)\) n/a 1904 8
3775.2.bl \(\chi_{3775}(491, \cdot)\) n/a 3024 8
3775.2.bm \(\chi_{3775}(571, \cdot)\) n/a 3024 8
3775.2.bn \(\chi_{3775}(16, \cdot)\) n/a 3024 8
3775.2.bo \(\chi_{3775}(306, \cdot)\) n/a 3024 8
3775.2.bp \(\chi_{3775}(831, \cdot)\) n/a 3024 8
3775.2.br \(\chi_{3775}(132, \cdot)\) n/a 1808 8
3775.2.bs \(\chi_{3775}(842, \cdot)\) n/a 3024 8
3775.2.bx \(\chi_{3775}(92, \cdot)\) n/a 3024 8
3775.2.by \(\chi_{3775}(87, \cdot)\) n/a 3024 8
3775.2.bz \(\chi_{3775}(452, \cdot)\) n/a 3024 8
3775.2.ca \(\chi_{3775}(1748, \cdot)\) n/a 3024 8
3775.2.cc \(\chi_{3775}(81, \cdot)\) n/a 7560 20
3775.2.cd \(\chi_{3775}(201, \cdot)\) n/a 4740 20
3775.2.ce \(\chi_{3775}(91, \cdot)\) n/a 7560 20
3775.2.cf \(\chi_{3775}(171, \cdot)\) n/a 7560 20
3775.2.cg \(\chi_{3775}(521, \cdot)\) n/a 7560 20
3775.2.ci \(\chi_{3775}(189, \cdot)\) n/a 3024 8
3775.2.cn \(\chi_{3775}(529, \cdot)\) n/a 3024 8
3775.2.co \(\chi_{3775}(4, \cdot)\) n/a 3024 8
3775.2.cp \(\chi_{3775}(1059, \cdot)\) n/a 3024 8
3775.2.cq \(\chi_{3775}(269, \cdot)\) n/a 3024 8
3775.2.cy \(\chi_{3775}(1224, \cdot)\) n/a 1808 8
3775.2.da \(\chi_{3775}(879, \cdot)\) n/a 7560 20
3775.2.df \(\chi_{3775}(29, \cdot)\) n/a 7560 20
3775.2.di \(\chi_{3775}(124, \cdot)\) n/a 4520 20
3775.2.dj \(\chi_{3775}(9, \cdot)\) n/a 7560 20
3775.2.dm \(\chi_{3775}(219, \cdot)\) n/a 7560 20
3775.2.dp \(\chi_{3775}(348, \cdot)\) n/a 6048 16
3775.2.dq \(\chi_{3775}(147, \cdot)\) n/a 6048 16
3775.2.dr \(\chi_{3775}(197, \cdot)\) n/a 6048 16
3775.2.ds \(\chi_{3775}(33, \cdot)\) n/a 6048 16
3775.2.dx \(\chi_{3775}(23, \cdot)\) n/a 6048 16
3775.2.dy \(\chi_{3775}(368, \cdot)\) n/a 3616 16
3775.2.ea \(\chi_{3775}(11, \cdot)\) n/a 15120 40
3775.2.eb \(\chi_{3775}(36, \cdot)\) n/a 15120 40
3775.2.ec \(\chi_{3775}(176, \cdot)\) n/a 9520 40
3775.2.ed \(\chi_{3775}(136, \cdot)\) n/a 15120 40
3775.2.ee \(\chi_{3775}(31, \cdot)\) n/a 15120 40
3775.2.eg \(\chi_{3775}(142, \cdot)\) n/a 15120 40
3775.2.eh \(\chi_{3775}(28, \cdot)\) n/a 15120 40
3775.2.em \(\chi_{3775}(53, \cdot)\) n/a 15120 40
3775.2.en \(\chi_{3775}(3, \cdot)\) n/a 15120 40
3775.2.eo \(\chi_{3775}(57, \cdot)\) n/a 9040 40
3775.2.er \(\chi_{3775}(254, \cdot)\) n/a 15120 40
3775.2.es \(\chi_{3775}(49, \cdot)\) n/a 9040 40
3775.2.ev \(\chi_{3775}(34, \cdot)\) n/a 15120 40
3775.2.ew \(\chi_{3775}(139, \cdot)\) n/a 15120 40
3775.2.fc \(\chi_{3775}(144, \cdot)\) n/a 15120 40
3775.2.ff \(\chi_{3775}(48, \cdot)\) n/a 30240 80
3775.2.fg \(\chi_{3775}(7, \cdot)\) n/a 18080 80
3775.2.fh \(\chi_{3775}(233, \cdot)\) n/a 30240 80
3775.2.fi \(\chi_{3775}(112, \cdot)\) n/a 30240 80
3775.2.fm \(\chi_{3775}(12, \cdot)\) n/a 30240 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3775))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3775)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(755))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3775))\)\(^{\oplus 1}\)