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Properties

Label 325.10
Level 325
Weight 10
Dimension 34199
Nonzero newspaces 24
Sturm bound 84000
Trace bound 3

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Defining parameters

Level: \( N \) = \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(84000\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(325))\).

Total New Old
Modular forms 38136 34649 3487
Cusp forms 37464 34199 3265
Eisenstein series 672 450 222

Trace form

\( 34199 q - 130 q^{2} + 526 q^{3} - 3146 q^{4} + 3454 q^{5} - 6554 q^{6} + 21658 q^{7} - 87322 q^{8} + 29730 q^{9} + O(q^{10}) \) \( 34199 q - 130 q^{2} + 526 q^{3} - 3146 q^{4} + 3454 q^{5} - 6554 q^{6} + 21658 q^{7} - 87322 q^{8} + 29730 q^{9} - 140896 q^{10} + 332466 q^{11} + 493824 q^{12} - 110328 q^{13} - 3231592 q^{14} - 326016 q^{15} + 8045670 q^{16} - 795989 q^{17} + 2211232 q^{18} - 4216726 q^{19} - 11172916 q^{20} + 9440406 q^{21} + 16778668 q^{22} + 1389810 q^{23} + 5357098 q^{24} + 14282434 q^{25} - 2154180 q^{26} - 24539252 q^{27} - 47464832 q^{28} + 888159 q^{29} + 37043764 q^{30} - 24134690 q^{31} + 4693992 q^{32} - 32795490 q^{33} + 95220974 q^{34} + 3615824 q^{35} - 46825590 q^{36} - 84127875 q^{37} - 303515500 q^{38} - 83776236 q^{39} + 294930728 q^{40} + 67542649 q^{41} + 43975024 q^{42} - 24043414 q^{43} - 415863236 q^{44} - 505527106 q^{45} - 112967270 q^{46} + 184137874 q^{47} + 904245594 q^{48} + 259479108 q^{49} + 1100057276 q^{50} - 719325180 q^{51} - 2071464288 q^{52} - 536409226 q^{53} + 582232592 q^{54} + 134681556 q^{55} + 2388993304 q^{56} + 485883530 q^{57} - 1089675478 q^{58} - 1761757542 q^{59} - 2474531908 q^{60} - 1346666543 q^{61} + 209994402 q^{62} + 4603239530 q^{63} + 9477808356 q^{64} + 3054186265 q^{65} + 3658300412 q^{66} - 2967583250 q^{67} - 11487389440 q^{68} - 11125759478 q^{69} - 7420983292 q^{70} - 1541920498 q^{71} + 582871332 q^{72} + 5557806318 q^{73} + 18840475182 q^{74} + 10728929704 q^{75} + 8553332790 q^{76} - 3612071808 q^{77} - 13841338508 q^{78} - 12518608488 q^{79} - 17418506092 q^{80} - 1267209192 q^{81} + 4989752946 q^{82} + 2279285022 q^{83} + 14211632792 q^{84} + 8071653134 q^{85} + 8440530780 q^{86} + 18724634690 q^{87} + 11260745024 q^{88} - 9189029028 q^{89} - 23154467196 q^{90} - 12574388992 q^{91} - 21134622144 q^{92} - 7109684366 q^{93} - 399939766 q^{94} - 497210516 q^{95} + 20600714096 q^{96} + 22371681842 q^{97} + 29443839538 q^{98} + 20930729670 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(325))\)

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
325.10.a \(\chi_{325}(1, \cdot)\) 325.10.a.a 4 1
325.10.a.b 5
325.10.a.c 7
325.10.a.d 9
325.10.a.e 10
325.10.a.f 10
325.10.a.g 17
325.10.a.h 17
325.10.a.i 19
325.10.a.j 19
325.10.a.k 27
325.10.a.l 27
325.10.b \(\chi_{325}(274, \cdot)\) n/a 162 1
325.10.c \(\chi_{325}(51, \cdot)\) n/a 196 1
325.10.d \(\chi_{325}(324, \cdot)\) n/a 188 1
325.10.e \(\chi_{325}(126, \cdot)\) n/a 394 2
325.10.f \(\chi_{325}(18, \cdot)\) n/a 374 2
325.10.k \(\chi_{325}(57, \cdot)\) n/a 374 2
325.10.l \(\chi_{325}(66, \cdot)\) n/a 1080 4
325.10.m \(\chi_{325}(49, \cdot)\) n/a 376 2
325.10.n \(\chi_{325}(101, \cdot)\) n/a 392 2
325.10.o \(\chi_{325}(74, \cdot)\) n/a 372 2
325.10.p \(\chi_{325}(64, \cdot)\) n/a 1248 4
325.10.q \(\chi_{325}(116, \cdot)\) n/a 1256 4
325.10.r \(\chi_{325}(14, \cdot)\) n/a 1080 4
325.10.s \(\chi_{325}(32, \cdot)\) n/a 748 4
325.10.x \(\chi_{325}(7, \cdot)\) n/a 748 4
325.10.y \(\chi_{325}(16, \cdot)\) n/a 2496 8
325.10.z \(\chi_{325}(8, \cdot)\) n/a 2504 8
325.10.be \(\chi_{325}(47, \cdot)\) n/a 2504 8
325.10.bf \(\chi_{325}(9, \cdot)\) n/a 2512 8
325.10.bg \(\chi_{325}(36, \cdot)\) n/a 2512 8
325.10.bh \(\chi_{325}(4, \cdot)\) n/a 2496 8
325.10.bi \(\chi_{325}(28, \cdot)\) n/a 5008 16
325.10.bn \(\chi_{325}(2, \cdot)\) n/a 5008 16

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(325))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(325)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 1}\)