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Properties

Label 525.3
Level 525
Weight 3
Dimension 12514
Nonzero newspaces 24
Sturm bound 57600
Trace bound 4

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Defining parameters

Level: \( N \) = \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(57600\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(525))\).

Total New Old
Modular forms 19872 12922 6950
Cusp forms 18528 12514 6014
Eisenstein series 1344 408 936

Trace form

\( 12514 q - 16 q^{2} - 38 q^{3} - 86 q^{4} - 8 q^{5} - 62 q^{6} - 66 q^{7} + 42 q^{8} + 24 q^{9} + O(q^{10}) \) \( 12514 q - 16 q^{2} - 38 q^{3} - 86 q^{4} - 8 q^{5} - 62 q^{6} - 66 q^{7} + 42 q^{8} + 24 q^{9} - 8 q^{10} + 70 q^{11} + 114 q^{12} - 30 q^{13} + 24 q^{14} - 108 q^{15} + 106 q^{16} + 168 q^{17} - 8 q^{18} + 178 q^{19} + 488 q^{20} - 6 q^{21} + 268 q^{22} + 208 q^{23} + 526 q^{24} + 152 q^{25} + 834 q^{26} + 532 q^{27} + 630 q^{28} + 68 q^{29} - 308 q^{30} - 426 q^{31} - 770 q^{32} - 294 q^{33} - 776 q^{34} - 332 q^{35} - 174 q^{36} + 64 q^{37} + 342 q^{38} - 6 q^{39} + 896 q^{40} - 256 q^{41} - 646 q^{42} - 100 q^{43} - 688 q^{44} + 368 q^{45} - 716 q^{46} - 14 q^{47} - 414 q^{48} - 8 q^{49} - 32 q^{50} + 72 q^{51} - 800 q^{52} - 508 q^{53} - 1336 q^{54} - 632 q^{55} + 1674 q^{56} - 328 q^{57} + 1064 q^{58} + 404 q^{59} - 2236 q^{60} + 1846 q^{61} + 776 q^{62} - 722 q^{63} + 718 q^{64} + 32 q^{65} - 796 q^{66} + 230 q^{67} + 148 q^{68} - 1460 q^{69} - 556 q^{70} - 1352 q^{71} - 1554 q^{72} - 1956 q^{73} - 2550 q^{74} - 356 q^{75} - 2148 q^{76} - 2056 q^{77} - 880 q^{78} - 1822 q^{79} - 2048 q^{80} + 408 q^{81} - 1812 q^{82} - 192 q^{83} - 1316 q^{84} + 2656 q^{85} - 830 q^{86} + 1352 q^{87} + 2440 q^{88} + 2940 q^{89} + 1596 q^{90} + 632 q^{91} + 3132 q^{92} - 308 q^{93} + 1852 q^{94} + 1568 q^{95} - 2770 q^{96} - 696 q^{97} - 758 q^{98} - 1104 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(525))\)

We only show spaces with odd 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
525.3.c \(\chi_{525}(176, \cdot)\) 525.3.c.a 4 1
525.3.c.b 16
525.3.c.c 16
525.3.c.d 16
525.3.c.e 24
525.3.e \(\chi_{525}(349, \cdot)\) 525.3.e.a 4 1
525.3.e.b 20
525.3.e.c 24
525.3.f \(\chi_{525}(449, \cdot)\) 525.3.f.a 8 1
525.3.f.b 32
525.3.f.c 32
525.3.h \(\chi_{525}(76, \cdot)\) 525.3.h.a 2 1
525.3.h.b 10
525.3.h.c 10
525.3.h.d 12
525.3.h.e 16
525.3.k \(\chi_{525}(293, \cdot)\) n/a 184 2
525.3.l \(\chi_{525}(43, \cdot)\) 525.3.l.a 8 2
525.3.l.b 8
525.3.l.c 16
525.3.l.d 16
525.3.l.e 24
525.3.o \(\chi_{525}(376, \cdot)\) 525.3.o.a 2 2
525.3.o.b 2
525.3.o.c 2
525.3.o.d 2
525.3.o.e 2
525.3.o.f 2
525.3.o.g 2
525.3.o.h 2
525.3.o.i 2
525.3.o.j 4
525.3.o.k 4
525.3.o.l 8
525.3.o.m 12
525.3.o.n 12
525.3.o.o 12
525.3.o.p 16
525.3.o.q 16
525.3.p \(\chi_{525}(74, \cdot)\) n/a 184 2
525.3.s \(\chi_{525}(124, \cdot)\) 525.3.s.a 4 2
525.3.s.b 4
525.3.s.c 4
525.3.s.d 4
525.3.s.e 4
525.3.s.f 4
525.3.s.g 8
525.3.s.h 16
525.3.s.i 24
525.3.s.j 24
525.3.u \(\chi_{525}(326, \cdot)\) n/a 190 2
525.3.v \(\chi_{525}(181, \cdot)\) n/a 320 4
525.3.x \(\chi_{525}(29, \cdot)\) n/a 480 4
525.3.y \(\chi_{525}(34, \cdot)\) n/a 320 4
525.3.ba \(\chi_{525}(71, \cdot)\) n/a 480 4
525.3.bd \(\chi_{525}(193, \cdot)\) n/a 192 4
525.3.be \(\chi_{525}(68, \cdot)\) n/a 368 4
525.3.bi \(\chi_{525}(22, \cdot)\) n/a 480 8
525.3.bj \(\chi_{525}(62, \cdot)\) n/a 1248 8
525.3.bl \(\chi_{525}(11, \cdot)\) n/a 1248 8
525.3.bn \(\chi_{525}(19, \cdot)\) n/a 640 8
525.3.bq \(\chi_{525}(44, \cdot)\) n/a 1248 8
525.3.br \(\chi_{525}(31, \cdot)\) n/a 640 8
525.3.bt \(\chi_{525}(17, \cdot)\) n/a 2496 16
525.3.bu \(\chi_{525}(37, \cdot)\) n/a 1280 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(525))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(525)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)