Properties

Label 275.6
Level 275
Weight 6
Dimension 13410
Nonzero newspaces 21
Sturm bound 36000
Trace bound 6

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Defining parameters

Level: \( N \) = \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 21 \)
Sturm bound: \(36000\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(275))\).

Total New Old
Modular forms 15280 13778 1502
Cusp forms 14720 13410 1310
Eisenstein series 560 368 192

Trace form

\( 13410 q - 37 q^{2} - 61 q^{3} - 253 q^{4} - 190 q^{5} + 935 q^{6} + 1018 q^{7} - 365 q^{8} - 2727 q^{9} + O(q^{10}) \) \( 13410 q - 37 q^{2} - 61 q^{3} - 253 q^{4} - 190 q^{5} + 935 q^{6} + 1018 q^{7} - 365 q^{8} - 2727 q^{9} - 840 q^{10} + 180 q^{11} + 18 q^{12} + 1604 q^{13} + 4164 q^{14} + 2380 q^{15} + 8775 q^{16} - 1182 q^{17} - 20856 q^{18} - 17360 q^{19} - 20580 q^{20} - 23270 q^{21} - 3777 q^{22} + 20039 q^{23} + 90745 q^{24} + 37950 q^{25} + 56620 q^{26} + 35765 q^{27} - 25634 q^{28} - 93260 q^{29} - 107740 q^{30} - 28945 q^{31} - 127452 q^{32} - 48861 q^{33} + 66494 q^{34} + 80680 q^{35} + 187380 q^{36} + 96323 q^{37} + 206340 q^{38} - 6984 q^{39} - 159080 q^{40} - 133380 q^{41} - 176654 q^{42} - 109066 q^{43} - 350688 q^{44} - 105530 q^{45} - 391230 q^{46} - 161092 q^{47} + 140224 q^{48} + 336512 q^{49} + 533300 q^{50} + 408830 q^{51} + 790278 q^{52} + 469424 q^{53} + 957810 q^{54} + 137670 q^{55} + 487860 q^{56} - 320380 q^{57} - 340660 q^{58} - 306975 q^{59} - 448500 q^{60} - 423180 q^{61} - 968834 q^{62} - 1148536 q^{63} - 1879373 q^{64} - 556150 q^{65} - 587030 q^{66} - 185167 q^{67} + 217406 q^{68} + 991311 q^{69} + 902260 q^{70} + 438485 q^{71} + 1525675 q^{72} + 269344 q^{73} + 766414 q^{74} + 621500 q^{75} + 984310 q^{76} + 651198 q^{77} + 931828 q^{78} + 571770 q^{79} - 4060 q^{80} - 555940 q^{81} + 103501 q^{82} - 472026 q^{83} - 1482556 q^{84} - 1362410 q^{85} - 1705545 q^{86} - 2213620 q^{87} - 1437935 q^{88} - 1085335 q^{89} - 327920 q^{90} + 1468400 q^{91} + 3045798 q^{92} + 1135573 q^{93} - 41786 q^{94} + 174380 q^{95} - 5011620 q^{96} - 424387 q^{97} - 1402624 q^{98} - 2144257 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(275))\)

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
275.6.a \(\chi_{275}(1, \cdot)\) 275.6.a.a 1 1
275.6.a.b 3
275.6.a.c 3
275.6.a.d 4
275.6.a.e 5
275.6.a.f 6
275.6.a.g 8
275.6.a.h 8
275.6.a.i 8
275.6.a.j 8
275.6.a.k 10
275.6.a.l 14
275.6.b \(\chi_{275}(199, \cdot)\) 275.6.b.a 2 1
275.6.b.b 6
275.6.b.c 6
275.6.b.d 8
275.6.b.e 10
275.6.b.f 12
275.6.b.g 16
275.6.b.h 16
275.6.e \(\chi_{275}(32, \cdot)\) n/a 176 2
275.6.g \(\chi_{275}(16, \cdot)\) n/a 592 4
275.6.h \(\chi_{275}(26, \cdot)\) n/a 368 4
275.6.i \(\chi_{275}(56, \cdot)\) n/a 504 4
275.6.j \(\chi_{275}(81, \cdot)\) n/a 592 4
275.6.k \(\chi_{275}(36, \cdot)\) n/a 592 4
275.6.l \(\chi_{275}(31, \cdot)\) n/a 592 4
275.6.n \(\chi_{275}(104, \cdot)\) n/a 592 4
275.6.t \(\chi_{275}(14, \cdot)\) n/a 592 4
275.6.y \(\chi_{275}(34, \cdot)\) n/a 496 4
275.6.z \(\chi_{275}(49, \cdot)\) n/a 352 4
275.6.ba \(\chi_{275}(4, \cdot)\) n/a 592 4
275.6.bb \(\chi_{275}(9, \cdot)\) n/a 592 4
275.6.bf \(\chi_{275}(28, \cdot)\) n/a 1184 8
275.6.bg \(\chi_{275}(13, \cdot)\) n/a 1184 8
275.6.bl \(\chi_{275}(17, \cdot)\) n/a 1184 8
275.6.bm \(\chi_{275}(7, \cdot)\) n/a 704 8
275.6.bn \(\chi_{275}(2, \cdot)\) n/a 1184 8
275.6.bo \(\chi_{275}(87, \cdot)\) n/a 1184 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(275))\) into lower level spaces

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