↑

Properties

Label 1175.4
Level 1175
Weight 4
Dimension 151567
Nonzero newspaces 12
Sturm bound 441600
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(441600\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1175))\).

Total New Old
Modular forms 166888 153411 13477
Cusp forms 164312 151567 12745
Eisenstein series 2576 1844 732

Trace form

\( 151567 q - 295 q^{2} - 271 q^{3} - 247 q^{4} - 358 q^{5} - 479 q^{6} - 255 q^{7} - 279 q^{8} - 371 q^{9} + O(q^{10}) \) \( 151567 q - 295 q^{2} - 271 q^{3} - 247 q^{4} - 358 q^{5} - 479 q^{6} - 255 q^{7} - 279 q^{8} - 371 q^{9} - 308 q^{10} - 319 q^{11} - 215 q^{12} - 431 q^{13} - 375 q^{14} - 368 q^{15} - 191 q^{16} + 465 q^{17} + 989 q^{18} + 361 q^{19} - 708 q^{20} - 879 q^{21} - 2231 q^{22} - 1471 q^{23} - 3139 q^{24} - 1738 q^{25} - 1159 q^{26} - 1759 q^{27} - 1527 q^{28} - 639 q^{29} + 212 q^{30} - 159 q^{31} + 2985 q^{32} + 1897 q^{33} + 2605 q^{34} + 1312 q^{35} - 4319 q^{36} + 843 q^{37} + 1905 q^{38} + 3607 q^{39} + 3752 q^{40} + 1665 q^{41} + 4517 q^{42} + 1711 q^{43} + 1765 q^{44} - 4758 q^{45} + 570 q^{46} - 921 q^{47} - 3030 q^{48} - 4057 q^{49} - 9368 q^{50} - 3329 q^{51} - 7603 q^{52} - 3509 q^{53} - 7599 q^{54} - 2188 q^{55} - 6335 q^{56} - 2775 q^{57} - 215 q^{58} + 5791 q^{59} + 22572 q^{60} + 1349 q^{61} + 21989 q^{62} + 15609 q^{63} + 13093 q^{64} + 3542 q^{65} + 1745 q^{66} - 1215 q^{67} - 7127 q^{68} - 7063 q^{69} - 8748 q^{70} - 3759 q^{71} - 18779 q^{72} - 9551 q^{73} - 19315 q^{74} - 12088 q^{75} - 17981 q^{76} - 18625 q^{77} - 31209 q^{78} - 12963 q^{79} - 12028 q^{80} - 4185 q^{81} + 4976 q^{82} + 13627 q^{83} + 27333 q^{84} + 18922 q^{85} + 16209 q^{86} + 21333 q^{87} + 42309 q^{88} + 21087 q^{89} + 15952 q^{90} + 22251 q^{91} + 25838 q^{92} - 930 q^{93} + 18451 q^{94} - 14356 q^{95} + 13789 q^{96} - 17323 q^{97} - 7256 q^{98} - 12473 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1175))\)

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
1175.4.a \(\chi_{1175}(1, \cdot)\) 1175.4.a.a 3 1
1175.4.a.b 8
1175.4.a.c 8
1175.4.a.d 10
1175.4.a.e 13
1175.4.a.f 15
1175.4.a.g 18
1175.4.a.h 18
1175.4.a.i 28
1175.4.a.j 28
1175.4.a.k 35
1175.4.a.l 35
1175.4.c \(\chi_{1175}(424, \cdot)\) n/a 206 1
1175.4.e \(\chi_{1175}(93, \cdot)\) n/a 428 2
1175.4.g \(\chi_{1175}(236, \cdot)\) n/a 1376 4
1175.4.i \(\chi_{1175}(189, \cdot)\) n/a 1384 4
1175.4.l \(\chi_{1175}(187, \cdot)\) n/a 2864 8
1175.4.m \(\chi_{1175}(51, \cdot)\) n/a 4950 22
1175.4.o \(\chi_{1175}(24, \cdot)\) n/a 4708 22
1175.4.r \(\chi_{1175}(43, \cdot)\) n/a 9416 44
1175.4.s \(\chi_{1175}(6, \cdot)\) n/a 31504 88
1175.4.u \(\chi_{1175}(4, \cdot)\) n/a 31504 88
1175.4.w \(\chi_{1175}(13, \cdot)\) n/a 63008 176

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1175))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1175)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(235))\)\(^{\oplus 2}\)