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Properties

Label 275.4
Level 275
Weight 4
Dimension 7972
Nonzero newspaces 21
Sturm bound 24000
Trace bound 6

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Defining parameters

Level: \( N \) = \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 21 \)
Sturm bound: \(24000\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(275))\).

Total New Old
Modular forms 9280 8340 940
Cusp forms 8720 7972 748
Eisenstein series 560 368 192

Trace form

\( 7972 q - 61 q^{2} - 37 q^{3} - 13 q^{4} - 70 q^{5} - 151 q^{6} - 31 q^{7} - 5 q^{8} - 57 q^{9} + O(q^{10}) \) \( 7972 q - 61 q^{2} - 37 q^{3} - 13 q^{4} - 70 q^{5} - 151 q^{6} - 31 q^{7} - 5 q^{8} - 57 q^{9} - 20 q^{10} + 27 q^{11} + 114 q^{12} - 177 q^{13} - 336 q^{14} - 80 q^{15} - 193 q^{16} + 549 q^{17} + 1218 q^{18} + 820 q^{19} - 420 q^{20} - 86 q^{21} - 401 q^{22} - 1402 q^{23} - 3095 q^{24} - 1450 q^{25} - 596 q^{26} - 1630 q^{27} - 1458 q^{28} - 455 q^{29} + 500 q^{30} - 171 q^{31} + 3444 q^{32} + 828 q^{33} + 2434 q^{34} + 1600 q^{35} + 1992 q^{36} + 2229 q^{37} + 3720 q^{38} + 5301 q^{39} + 5320 q^{40} + 1449 q^{41} + 9358 q^{42} + 6698 q^{43} + 6972 q^{44} - 2390 q^{45} + 514 q^{46} - 4711 q^{47} - 15032 q^{48} - 9473 q^{49} - 11800 q^{50} - 12706 q^{51} - 25346 q^{52} - 11587 q^{53} - 26430 q^{54} - 5310 q^{55} - 18060 q^{56} - 7210 q^{57} - 8260 q^{58} + 5790 q^{59} + 19020 q^{60} + 3899 q^{61} + 25138 q^{62} + 19628 q^{63} + 25547 q^{64} + 7190 q^{65} + 14794 q^{66} + 12044 q^{67} + 14942 q^{68} + 6576 q^{69} - 1020 q^{70} - 2911 q^{71} - 9725 q^{72} - 11867 q^{73} - 20546 q^{74} - 11800 q^{75} - 7250 q^{76} - 7341 q^{77} - 12524 q^{78} - 2505 q^{79} - 11740 q^{80} + 3572 q^{81} + 10303 q^{82} + 15168 q^{83} + 28484 q^{84} + 19210 q^{85} + 10689 q^{86} + 20390 q^{87} + 17225 q^{88} + 16490 q^{89} + 30820 q^{90} + 22679 q^{91} + 44334 q^{92} + 27181 q^{93} + 22494 q^{94} - 5620 q^{95} + 31524 q^{96} - 12406 q^{97} - 10138 q^{98} - 11377 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(275))\)

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
275.4.a \(\chi_{275}(1, \cdot)\) 275.4.a.a 1 1
275.4.a.b 2
275.4.a.c 2
275.4.a.d 3
275.4.a.e 4
275.4.a.f 5
275.4.a.g 5
275.4.a.h 5
275.4.a.i 5
275.4.a.j 6
275.4.a.k 10
275.4.b \(\chi_{275}(199, \cdot)\) 275.4.b.a 2 1
275.4.b.b 4
275.4.b.c 4
275.4.b.d 6
275.4.b.e 8
275.4.b.f 10
275.4.b.g 10
275.4.e \(\chi_{275}(32, \cdot)\) n/a 104 2
275.4.g \(\chi_{275}(16, \cdot)\) n/a 352 4
275.4.h \(\chi_{275}(26, \cdot)\) n/a 216 4
275.4.i \(\chi_{275}(56, \cdot)\) n/a 296 4
275.4.j \(\chi_{275}(81, \cdot)\) n/a 352 4
275.4.k \(\chi_{275}(36, \cdot)\) n/a 352 4
275.4.l \(\chi_{275}(31, \cdot)\) n/a 352 4
275.4.n \(\chi_{275}(104, \cdot)\) n/a 352 4
275.4.t \(\chi_{275}(14, \cdot)\) n/a 352 4
275.4.y \(\chi_{275}(34, \cdot)\) n/a 304 4
275.4.z \(\chi_{275}(49, \cdot)\) n/a 208 4
275.4.ba \(\chi_{275}(4, \cdot)\) n/a 352 4
275.4.bb \(\chi_{275}(9, \cdot)\) n/a 352 4
275.4.bf \(\chi_{275}(28, \cdot)\) n/a 704 8
275.4.bg \(\chi_{275}(13, \cdot)\) n/a 704 8
275.4.bl \(\chi_{275}(17, \cdot)\) n/a 704 8
275.4.bm \(\chi_{275}(7, \cdot)\) n/a 416 8
275.4.bn \(\chi_{275}(2, \cdot)\) n/a 704 8
275.4.bo \(\chi_{275}(87, \cdot)\) n/a 704 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(275))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(275)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 1}\)