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Properties

Label 528.5
Level 528
Weight 5
Dimension 12664
Nonzero newspaces 16
Sturm bound 76800
Trace bound 11

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Defining parameters

Level: \( N \) = \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(76800\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(528))\).

Total New Old
Modular forms 31280 12824 18456
Cusp forms 30160 12664 17496
Eisenstein series 1120 160 960

Trace form

\( 12664 q - 13 q^{3} - 56 q^{4} + 144 q^{5} + 116 q^{6} - 66 q^{7} - 360 q^{8} + 101 q^{9} + O(q^{10}) \) \( 12664 q - 13 q^{3} - 56 q^{4} + 144 q^{5} + 116 q^{6} - 66 q^{7} - 360 q^{8} + 101 q^{9} - 424 q^{10} + 192 q^{11} - 696 q^{12} + 1034 q^{13} + 312 q^{14} - 519 q^{15} + 1208 q^{16} - 720 q^{17} - 404 q^{18} - 2714 q^{19} + 2400 q^{20} - 1082 q^{21} + 736 q^{22} + 4608 q^{23} - 748 q^{24} - 720 q^{25} - 5400 q^{26} - 2797 q^{27} - 7720 q^{28} - 1584 q^{29} - 3308 q^{30} + 5006 q^{31} + 6720 q^{32} - 5193 q^{33} + 20640 q^{34} + 13248 q^{35} + 3404 q^{36} + 3626 q^{37} + 11760 q^{38} + 7405 q^{39} - 6712 q^{40} + 7152 q^{41} - 10540 q^{42} - 20560 q^{43} - 18840 q^{44} - 13802 q^{45} - 15208 q^{46} - 18720 q^{47} + 3884 q^{48} - 9540 q^{49} + 51768 q^{50} + 17585 q^{51} + 56504 q^{52} + 20592 q^{53} - 14140 q^{54} + 21378 q^{55} - 30912 q^{56} + 27375 q^{57} - 34232 q^{58} - 26112 q^{59} - 23300 q^{60} - 36278 q^{61} - 43704 q^{62} - 49779 q^{63} - 16424 q^{64} - 36576 q^{65} - 1968 q^{66} - 4408 q^{67} + 34560 q^{68} + 22340 q^{69} + 130512 q^{70} + 116352 q^{71} + 23356 q^{72} + 104330 q^{73} + 6192 q^{74} + 87819 q^{75} - 83208 q^{76} - 75648 q^{77} - 154376 q^{78} - 72882 q^{79} - 313416 q^{80} + 51333 q^{81} - 151048 q^{82} - 108000 q^{83} - 18484 q^{84} - 154642 q^{85} - 52320 q^{86} - 62966 q^{87} + 100632 q^{88} + 17520 q^{89} + 108748 q^{90} - 53862 q^{91} + 277728 q^{92} + 86419 q^{93} + 486440 q^{94} + 100800 q^{95} + 185940 q^{96} + 264394 q^{97} + 257064 q^{98} + 56597 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(528))\)

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
528.5.c \(\chi_{528}(199, \cdot)\) None 0 1
528.5.e \(\chi_{528}(505, \cdot)\) None 0 1
528.5.g \(\chi_{528}(527, \cdot)\) 528.5.g.a 2 1
528.5.g.b 2
528.5.g.c 2
528.5.g.d 2
528.5.g.e 4
528.5.g.f 4
528.5.g.g 24
528.5.g.h 56
528.5.i \(\chi_{528}(353, \cdot)\) 528.5.i.a 2 1
528.5.i.b 12
528.5.i.c 12
528.5.i.d 14
528.5.i.e 40
528.5.j \(\chi_{528}(241, \cdot)\) 528.5.j.a 8 1
528.5.j.b 8
528.5.j.c 8
528.5.j.d 24
528.5.l \(\chi_{528}(463, \cdot)\) 528.5.l.a 12 1
528.5.l.b 12
528.5.l.c 16
528.5.n \(\chi_{528}(89, \cdot)\) None 0 1
528.5.p \(\chi_{528}(263, \cdot)\) None 0 1
528.5.r \(\chi_{528}(221, \cdot)\) n/a 640 2
528.5.s \(\chi_{528}(131, \cdot)\) n/a 760 2
528.5.v \(\chi_{528}(109, \cdot)\) n/a 384 2
528.5.w \(\chi_{528}(67, \cdot)\) n/a 320 2
528.5.z \(\chi_{528}(167, \cdot)\) None 0 4
528.5.bb \(\chi_{528}(137, \cdot)\) None 0 4
528.5.bd \(\chi_{528}(31, \cdot)\) n/a 192 4
528.5.bf \(\chi_{528}(145, \cdot)\) n/a 192 4
528.5.bg \(\chi_{528}(113, \cdot)\) n/a 376 4
528.5.bi \(\chi_{528}(95, \cdot)\) n/a 384 4
528.5.bk \(\chi_{528}(73, \cdot)\) None 0 4
528.5.bm \(\chi_{528}(103, \cdot)\) None 0 4
528.5.bp \(\chi_{528}(91, \cdot)\) n/a 1536 8
528.5.bq \(\chi_{528}(13, \cdot)\) n/a 1536 8
528.5.bt \(\chi_{528}(35, \cdot)\) n/a 3040 8
528.5.bu \(\chi_{528}(5, \cdot)\) n/a 3040 8

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(528))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(528)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 2}\)