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Properties

Label 663.4
Level 663
Weight 4
Dimension 35276
Nonzero newspaces 36
Sturm bound 129024
Trace bound 17

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Defining parameters

Level: \( N \) = \( 663 = 3 \cdot 13 \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(129024\)
Trace bound: \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(663))\).

Total New Old
Modular forms 49152 35932 13220
Cusp forms 47616 35276 12340
Eisenstein series 1536 656 880

Trace form

\( 35276 q - 68 q^{3} - 136 q^{4} - 68 q^{6} - 280 q^{7} - 288 q^{8} - 68 q^{9} + O(q^{10}) \) \( 35276 q - 68 q^{3} - 136 q^{4} - 68 q^{6} - 280 q^{7} - 288 q^{8} - 68 q^{9} - 192 q^{10} - 208 q^{11} + 208 q^{12} + 488 q^{13} + 1120 q^{14} + 748 q^{15} + 1624 q^{16} + 134 q^{17} - 584 q^{18} - 1592 q^{19} - 1616 q^{20} - 260 q^{21} + 528 q^{22} + 80 q^{23} - 1508 q^{24} - 3572 q^{25} + 936 q^{26} + 1504 q^{27} + 2528 q^{28} + 1820 q^{29} + 4732 q^{30} + 3080 q^{31} + 2920 q^{32} + 252 q^{33} + 6044 q^{34} + 848 q^{35} - 5464 q^{36} + 1268 q^{37} + 2080 q^{38} - 2172 q^{39} - 10384 q^{40} - 6796 q^{41} - 6704 q^{42} - 8296 q^{43} - 10456 q^{44} - 2368 q^{45} - 2968 q^{46} + 2976 q^{47} - 820 q^{48} + 7784 q^{49} + 8832 q^{50} - 832 q^{51} + 2960 q^{52} - 3072 q^{53} - 16932 q^{54} - 5912 q^{55} - 4856 q^{56} - 3196 q^{57} - 1184 q^{58} + 1328 q^{59} + 12656 q^{60} + 140 q^{61} + 9560 q^{62} + 24340 q^{63} + 4752 q^{64} + 2460 q^{65} + 21456 q^{66} + 7928 q^{67} + 19240 q^{68} + 10676 q^{69} + 6848 q^{70} + 1824 q^{71} + 1096 q^{72} - 1240 q^{73} - 10488 q^{74} - 14144 q^{75} - 23144 q^{76} - 14080 q^{77} - 31080 q^{78} - 12752 q^{79} - 18080 q^{80} - 24180 q^{81} - 1248 q^{82} - 11824 q^{83} + 8832 q^{84} + 4526 q^{85} - 2272 q^{86} + 12580 q^{87} + 35264 q^{88} - 816 q^{89} + 10544 q^{90} + 3064 q^{91} + 21680 q^{92} + 12084 q^{93} + 19544 q^{94} + 10832 q^{95} + 3224 q^{96} + 12680 q^{97} + 4920 q^{98} - 3388 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(663))\)

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
663.4.a \(\chi_{663}(1, \cdot)\) 663.4.a.a 1 1
663.4.a.b 2
663.4.a.c 7
663.4.a.d 9
663.4.a.e 10
663.4.a.f 11
663.4.a.g 13
663.4.a.h 13
663.4.a.i 15
663.4.a.j 15
663.4.b \(\chi_{663}(103, \cdot)\) n/a 112 1
663.4.e \(\chi_{663}(220, \cdot)\) n/a 128 1
663.4.f \(\chi_{663}(118, \cdot)\) n/a 108 1
663.4.i \(\chi_{663}(256, \cdot)\) n/a 224 2
663.4.j \(\chi_{663}(157, \cdot)\) n/a 216 2
663.4.m \(\chi_{663}(200, \cdot)\) n/a 496 2
663.4.n \(\chi_{663}(86, \cdot)\) n/a 448 2
663.4.q \(\chi_{663}(203, \cdot)\) n/a 496 2
663.4.r \(\chi_{663}(47, \cdot)\) n/a 496 2
663.4.u \(\chi_{663}(64, \cdot)\) n/a 256 2
663.4.w \(\chi_{663}(16, \cdot)\) n/a 248 2
663.4.z \(\chi_{663}(205, \cdot)\) n/a 224 2
663.4.ba \(\chi_{663}(322, \cdot)\) n/a 256 2
663.4.bd \(\chi_{663}(8, \cdot)\) n/a 992 4
663.4.bg \(\chi_{663}(196, \cdot)\) n/a 432 4
663.4.bh \(\chi_{663}(25, \cdot)\) n/a 496 4
663.4.bi \(\chi_{663}(161, \cdot)\) n/a 992 4
663.4.bk \(\chi_{663}(4, \cdot)\) n/a 512 4
663.4.bm \(\chi_{663}(89, \cdot)\) n/a 992 4
663.4.bp \(\chi_{663}(50, \cdot)\) n/a 992 4
663.4.bq \(\chi_{663}(137, \cdot)\) n/a 896 4
663.4.bt \(\chi_{663}(98, \cdot)\) n/a 992 4
663.4.bv \(\chi_{663}(55, \cdot)\) n/a 496 4
663.4.bx \(\chi_{663}(116, \cdot)\) n/a 1984 8
663.4.by \(\chi_{663}(14, \cdot)\) n/a 1728 8
663.4.ca \(\chi_{663}(31, \cdot)\) n/a 1008 8
663.4.cd \(\chi_{663}(73, \cdot)\) n/a 1008 8
663.4.cf \(\chi_{663}(110, \cdot)\) n/a 1984 8
663.4.cg \(\chi_{663}(94, \cdot)\) n/a 1024 8
663.4.ch \(\chi_{663}(43, \cdot)\) n/a 992 8
663.4.ck \(\chi_{663}(2, \cdot)\) n/a 1984 8
663.4.cm \(\chi_{663}(7, \cdot)\) n/a 2016 16
663.4.cp \(\chi_{663}(28, \cdot)\) n/a 2016 16
663.4.cr \(\chi_{663}(29, \cdot)\) n/a 3968 16
663.4.cs \(\chi_{663}(23, \cdot)\) n/a 3968 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(663))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(663)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(221))\)\(^{\oplus 2}\)