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Properties

Label 700.4
Level 700
Weight 4
Dimension 22054
Nonzero newspaces 24
Sturm bound 115200
Trace bound 7

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Defining parameters

Level: \( N \) = \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(115200\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(700))\).

Total New Old
Modular forms 44040 22466 21574
Cusp forms 42360 22054 20306
Eisenstein series 1680 412 1268

Trace form

\( 22054 q - 27 q^{2} + 10 q^{3} - 19 q^{4} - 26 q^{5} + 8 q^{6} - 8 q^{7} - 183 q^{8} - 432 q^{9} + O(q^{10}) \) \( 22054 q - 27 q^{2} + 10 q^{3} - 19 q^{4} - 26 q^{5} + 8 q^{6} - 8 q^{7} - 183 q^{8} - 432 q^{9} - 176 q^{10} - 164 q^{11} - 504 q^{12} + 330 q^{13} - 185 q^{14} + 344 q^{15} + 625 q^{16} + 204 q^{17} + 1229 q^{18} + 62 q^{19} + 604 q^{20} + 206 q^{21} + 1514 q^{22} - 604 q^{23} + 312 q^{24} - 670 q^{25} - 1508 q^{26} - 716 q^{27} - 1141 q^{28} - 2052 q^{29} - 2508 q^{30} - 1088 q^{31} - 1707 q^{32} - 1692 q^{33} - 40 q^{34} - 596 q^{35} + 1449 q^{36} - 258 q^{37} - 216 q^{38} - 2040 q^{39} - 456 q^{40} + 2360 q^{41} - 410 q^{42} + 1540 q^{43} + 562 q^{44} + 7010 q^{45} - 2470 q^{46} + 6752 q^{47} + 1324 q^{48} + 2346 q^{49} + 4316 q^{50} + 1820 q^{51} + 2684 q^{52} - 358 q^{53} + 6912 q^{54} - 1904 q^{55} - 2837 q^{56} - 10996 q^{57} - 1970 q^{58} - 4258 q^{59} - 8188 q^{60} - 5854 q^{61} + 1852 q^{62} + 2168 q^{63} - 247 q^{64} - 1358 q^{65} + 1944 q^{66} + 5840 q^{67} + 1876 q^{68} + 3988 q^{69} + 9342 q^{70} + 5912 q^{71} + 8525 q^{72} + 14236 q^{73} + 10986 q^{74} - 3640 q^{75} + 11936 q^{76} + 1348 q^{77} + 17048 q^{78} - 7972 q^{79} - 264 q^{80} - 4348 q^{81} + 5500 q^{82} - 12426 q^{83} - 5150 q^{84} - 14954 q^{85} - 12410 q^{86} + 3364 q^{87} - 10414 q^{88} + 5386 q^{89} - 9628 q^{90} + 5942 q^{91} - 19378 q^{92} + 7312 q^{93} - 28876 q^{94} + 3064 q^{95} - 24856 q^{96} + 7896 q^{97} - 21421 q^{98} - 9676 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(700))\)

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
700.4.a \(\chi_{700}(1, \cdot)\) 700.4.a.a 1 1
700.4.a.b 1
700.4.a.c 1
700.4.a.d 1
700.4.a.e 1
700.4.a.f 1
700.4.a.g 1
700.4.a.h 1
700.4.a.i 1
700.4.a.j 1
700.4.a.k 1
700.4.a.l 1
700.4.a.m 1
700.4.a.n 1
700.4.a.o 2
700.4.a.p 2
700.4.a.q 2
700.4.a.r 2
700.4.a.s 3
700.4.a.t 3
700.4.c \(\chi_{700}(699, \cdot)\) n/a 212 1
700.4.e \(\chi_{700}(449, \cdot)\) 700.4.e.a 2 1
700.4.e.b 2
700.4.e.c 2
700.4.e.d 2
700.4.e.e 2
700.4.e.f 2
700.4.e.g 2
700.4.e.h 2
700.4.e.i 2
700.4.e.j 4
700.4.e.k 6
700.4.g \(\chi_{700}(251, \cdot)\) n/a 222 1
700.4.i \(\chi_{700}(401, \cdot)\) 700.4.i.a 2 2
700.4.i.b 2
700.4.i.c 2
700.4.i.d 2
700.4.i.e 4
700.4.i.f 4
700.4.i.g 4
700.4.i.h 4
700.4.i.i 14
700.4.i.j 14
700.4.i.k 24
700.4.k \(\chi_{700}(43, \cdot)\) n/a 324 2
700.4.m \(\chi_{700}(293, \cdot)\) 700.4.m.a 8 2
700.4.m.b 8
700.4.m.c 24
700.4.m.d 32
700.4.n \(\chi_{700}(141, \cdot)\) n/a 184 4
700.4.p \(\chi_{700}(451, \cdot)\) n/a 444 2
700.4.r \(\chi_{700}(149, \cdot)\) 700.4.r.a 4 2
700.4.r.b 4
700.4.r.c 4
700.4.r.d 8
700.4.r.e 8
700.4.r.f 8
700.4.r.g 8
700.4.r.h 28
700.4.t \(\chi_{700}(199, \cdot)\) n/a 424 2
700.4.w \(\chi_{700}(111, \cdot)\) n/a 1424 4
700.4.y \(\chi_{700}(29, \cdot)\) n/a 176 4
700.4.ba \(\chi_{700}(139, \cdot)\) n/a 1424 4
700.4.bc \(\chi_{700}(157, \cdot)\) n/a 144 4
700.4.be \(\chi_{700}(107, \cdot)\) n/a 848 4
700.4.bg \(\chi_{700}(81, \cdot)\) n/a 480 8
700.4.bh \(\chi_{700}(13, \cdot)\) n/a 480 8
700.4.bj \(\chi_{700}(127, \cdot)\) n/a 2160 8
700.4.bm \(\chi_{700}(19, \cdot)\) n/a 2848 8
700.4.bo \(\chi_{700}(9, \cdot)\) n/a 480 8
700.4.bq \(\chi_{700}(31, \cdot)\) n/a 2848 8
700.4.bt \(\chi_{700}(23, \cdot)\) n/a 5696 16
700.4.bv \(\chi_{700}(17, \cdot)\) n/a 960 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(700))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(700)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)