↑

Properties

Label 2175.4
Level 2175
Weight 4
Dimension 346454
Nonzero newspaces 40
Sturm bound 1344000
Trace bound 6

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(1344000\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2175))\).

Total New Old
Modular forms 507136 348670 158466
Cusp forms 500864 346454 154410
Eisenstein series 6272 2216 4056

Trace form

\( 346454 q + 16 q^{2} - 186 q^{3} - 420 q^{4} + 12 q^{5} - 258 q^{6} - 404 q^{7} - 144 q^{8} - 234 q^{9} + O(q^{10}) \) \( 346454 q + 16 q^{2} - 186 q^{3} - 420 q^{4} + 12 q^{5} - 258 q^{6} - 404 q^{7} - 144 q^{8} - 234 q^{9} - 600 q^{10} - 224 q^{11} + 270 q^{12} + 332 q^{13} + 1056 q^{14} + 144 q^{15} - 324 q^{16} - 1120 q^{17} - 1338 q^{18} - 1828 q^{19} - 312 q^{20} - 1346 q^{21} + 1260 q^{22} + 664 q^{23} + 874 q^{24} + 2644 q^{25} + 1148 q^{26} + 1554 q^{27} + 2232 q^{28} + 168 q^{29} + 1324 q^{30} - 660 q^{31} - 5808 q^{32} - 2466 q^{33} - 9056 q^{34} - 4480 q^{35} - 1714 q^{36} - 6272 q^{37} - 8056 q^{38} - 5242 q^{39} - 8912 q^{40} - 3296 q^{41} - 410 q^{42} + 2604 q^{43} + 11732 q^{44} + 4688 q^{45} + 20432 q^{46} + 10776 q^{47} + 12794 q^{48} + 10736 q^{49} + 16448 q^{50} + 2506 q^{51} + 9364 q^{52} + 2446 q^{53} + 6514 q^{54} + 2584 q^{55} - 9100 q^{56} - 476 q^{57} - 22604 q^{58} - 7656 q^{59} - 372 q^{60} - 7732 q^{61} - 27404 q^{62} - 190 q^{63} - 18528 q^{64} - 2444 q^{65} + 2910 q^{66} + 3868 q^{67} + 10996 q^{68} - 1546 q^{69} - 3528 q^{70} + 4248 q^{71} - 33830 q^{72} + 566 q^{73} - 7484 q^{74} - 19016 q^{75} - 18764 q^{76} - 6912 q^{77} - 15374 q^{78} - 6404 q^{79} + 2008 q^{80} + 6550 q^{81} - 17796 q^{82} - 22208 q^{83} + 4920 q^{84} - 25524 q^{85} - 2384 q^{86} + 3876 q^{87} - 7792 q^{88} - 6804 q^{89} + 21564 q^{90} + 14492 q^{91} + 21424 q^{92} + 29118 q^{93} + 57500 q^{94} + 31888 q^{95} + 40352 q^{96} + 83938 q^{97} + 82676 q^{98} + 16534 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2175))\)

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
2175.4.a \(\chi_{2175}(1, \cdot)\) 2175.4.a.a 1 1
2175.4.a.b 1
2175.4.a.c 1
2175.4.a.d 2
2175.4.a.e 2
2175.4.a.f 2
2175.4.a.g 2
2175.4.a.h 5
2175.4.a.i 5
2175.4.a.j 5
2175.4.a.k 6
2175.4.a.l 6
2175.4.a.m 7
2175.4.a.n 7
2175.4.a.o 8
2175.4.a.p 10
2175.4.a.q 10
2175.4.a.r 10
2175.4.a.s 12
2175.4.a.t 12
2175.4.a.u 16
2175.4.a.v 16
2175.4.a.w 18
2175.4.a.x 18
2175.4.a.y 21
2175.4.a.z 21
2175.4.a.ba 21
2175.4.a.bb 21
2175.4.c \(\chi_{2175}(349, \cdot)\) n/a 252 1
2175.4.d \(\chi_{2175}(376, \cdot)\) n/a 284 1
2175.4.f \(\chi_{2175}(724, \cdot)\) n/a 272 1
2175.4.j \(\chi_{2175}(157, \cdot)\) n/a 540 2
2175.4.l \(\chi_{2175}(824, \cdot)\) n/a 1072 2
2175.4.m \(\chi_{2175}(407, \cdot)\) n/a 1008 2
2175.4.p \(\chi_{2175}(782, \cdot)\) n/a 1072 2
2175.4.q \(\chi_{2175}(476, \cdot)\) n/a 1128 2
2175.4.s \(\chi_{2175}(307, \cdot)\) n/a 540 2
2175.4.u \(\chi_{2175}(436, \cdot)\) n/a 1680 4
2175.4.v \(\chi_{2175}(226, \cdot)\) n/a 1716 6
2175.4.x \(\chi_{2175}(289, \cdot)\) n/a 1792 4
2175.4.z \(\chi_{2175}(784, \cdot)\) n/a 1680 4
2175.4.bc \(\chi_{2175}(811, \cdot)\) n/a 1808 4
2175.4.bf \(\chi_{2175}(274, \cdot)\) n/a 1632 6
2175.4.bh \(\chi_{2175}(151, \cdot)\) n/a 1704 6
2175.4.bi \(\chi_{2175}(49, \cdot)\) n/a 1608 6
2175.4.bl \(\chi_{2175}(742, \cdot)\) n/a 3600 8
2175.4.bm \(\chi_{2175}(104, \cdot)\) n/a 7168 8
2175.4.bo \(\chi_{2175}(173, \cdot)\) n/a 7168 8
2175.4.br \(\chi_{2175}(233, \cdot)\) n/a 6720 8
2175.4.bt \(\chi_{2175}(41, \cdot)\) n/a 7168 8
2175.4.bu \(\chi_{2175}(133, \cdot)\) n/a 3600 8
2175.4.bx \(\chi_{2175}(757, \cdot)\) n/a 3240 12
2175.4.bz \(\chi_{2175}(26, \cdot)\) n/a 6768 12
2175.4.ca \(\chi_{2175}(332, \cdot)\) n/a 6432 12
2175.4.cd \(\chi_{2175}(107, \cdot)\) n/a 6432 12
2175.4.ce \(\chi_{2175}(224, \cdot)\) n/a 6432 12
2175.4.cg \(\chi_{2175}(43, \cdot)\) n/a 3240 12
2175.4.ci \(\chi_{2175}(16, \cdot)\) n/a 10752 24
2175.4.cj \(\chi_{2175}(91, \cdot)\) n/a 10848 24
2175.4.cm \(\chi_{2175}(94, \cdot)\) n/a 10848 24
2175.4.co \(\chi_{2175}(4, \cdot)\) n/a 10752 24
2175.4.cr \(\chi_{2175}(37, \cdot)\) n/a 21600 48
2175.4.cs \(\chi_{2175}(11, \cdot)\) n/a 43008 48
2175.4.cu \(\chi_{2175}(23, \cdot)\) n/a 43008 48
2175.4.cx \(\chi_{2175}(38, \cdot)\) n/a 43008 48
2175.4.cz \(\chi_{2175}(14, \cdot)\) n/a 43008 48
2175.4.da \(\chi_{2175}(73, \cdot)\) n/a 21600 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2175))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2175)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(435))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(725))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2175))\)\(^{\oplus 1}\)