Properties

Label 630.3
Level 630
Weight 3
Dimension 4812
Nonzero newspaces 30
Sturm bound 62208
Trace bound 11

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(62208\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(630))\).

Total New Old
Modular forms 21504 4812 16692
Cusp forms 19968 4812 15156
Eisenstein series 1536 0 1536

Trace form

\( 4812 q + 4 q^{2} + 8 q^{4} - 30 q^{5} - 48 q^{6} - 32 q^{7} - 8 q^{8} - 32 q^{9} + O(q^{10}) \) \( 4812 q + 4 q^{2} + 8 q^{4} - 30 q^{5} - 48 q^{6} - 32 q^{7} - 8 q^{8} - 32 q^{9} - 108 q^{10} - 124 q^{11} + 16 q^{12} - 164 q^{13} - 144 q^{14} - 36 q^{15} - 32 q^{16} - 112 q^{17} - 64 q^{18} - 92 q^{19} + 80 q^{20} + 36 q^{21} + 128 q^{22} + 356 q^{23} + 96 q^{24} - 210 q^{25} + 360 q^{26} + 408 q^{27} + 80 q^{28} + 600 q^{29} + 264 q^{30} + 60 q^{31} - 16 q^{32} + 376 q^{33} + 80 q^{34} + 166 q^{35} + 304 q^{36} + 48 q^{37} + 296 q^{38} + 568 q^{39} - 24 q^{40} + 440 q^{41} + 32 q^{42} + 240 q^{43} + 168 q^{44} - 76 q^{45} + 488 q^{46} + 492 q^{47} - 32 q^{48} + 132 q^{49} - 100 q^{50} + 864 q^{51} - 200 q^{52} + 1264 q^{53} + 336 q^{54} + 536 q^{55} - 64 q^{56} + 224 q^{57} - 416 q^{58} - 180 q^{59} - 152 q^{60} - 1500 q^{61} - 944 q^{62} - 236 q^{63} - 256 q^{64} - 1272 q^{65} - 1824 q^{66} - 404 q^{67} - 784 q^{68} - 2344 q^{69} + 24 q^{70} - 1952 q^{71} - 384 q^{72} - 64 q^{73} - 768 q^{74} + 156 q^{75} + 752 q^{76} - 712 q^{77} - 640 q^{78} + 260 q^{79} - 24 q^{80} + 1088 q^{81} + 1280 q^{82} + 1584 q^{83} - 48 q^{84} + 1720 q^{85} + 1344 q^{86} + 1840 q^{87} + 464 q^{88} + 2844 q^{89} + 1888 q^{90} + 3088 q^{91} + 784 q^{92} + 1520 q^{93} + 1000 q^{94} + 2326 q^{95} + 256 q^{96} + 2500 q^{97} + 708 q^{98} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(630))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
630.3.c \(\chi_{630}(449, \cdot)\) 630.3.c.a 24 1
630.3.e \(\chi_{630}(71, \cdot)\) 630.3.e.a 8 1
630.3.e.b 8
630.3.f \(\chi_{630}(181, \cdot)\) 630.3.f.a 8 1
630.3.f.b 8
630.3.f.c 8
630.3.h \(\chi_{630}(559, \cdot)\) 630.3.h.a 4 1
630.3.h.b 4
630.3.h.c 8
630.3.h.d 8
630.3.h.e 16
630.3.n \(\chi_{630}(377, \cdot)\) 630.3.n.a 32 2
630.3.n.b 32
630.3.o \(\chi_{630}(127, \cdot)\) 630.3.o.a 4 2
630.3.o.b 8
630.3.o.c 8
630.3.o.d 12
630.3.o.e 12
630.3.o.f 16
630.3.q \(\chi_{630}(191, \cdot)\) n/a 128 2
630.3.s \(\chi_{630}(569, \cdot)\) n/a 192 2
630.3.v \(\chi_{630}(271, \cdot)\) 630.3.v.a 8 2
630.3.v.b 8
630.3.v.c 16
630.3.v.d 24
630.3.w \(\chi_{630}(229, \cdot)\) n/a 192 2
630.3.x \(\chi_{630}(139, \cdot)\) n/a 192 2
630.3.y \(\chi_{630}(391, \cdot)\) n/a 128 2
630.3.bb \(\chi_{630}(241, \cdot)\) n/a 128 2
630.3.bc \(\chi_{630}(19, \cdot)\) 630.3.bc.a 16 2
630.3.bc.b 32
630.3.bc.c 32
630.3.bd \(\chi_{630}(179, \cdot)\) 630.3.bd.a 8 2
630.3.bd.b 8
630.3.bd.c 48
630.3.bg \(\chi_{630}(281, \cdot)\) 630.3.bg.a 96 2
630.3.bh \(\chi_{630}(11, \cdot)\) n/a 128 2
630.3.bj \(\chi_{630}(149, \cdot)\) n/a 192 2
630.3.bm \(\chi_{630}(29, \cdot)\) n/a 144 2
630.3.bn \(\chi_{630}(431, \cdot)\) 630.3.bn.a 24 2
630.3.bn.b 24
630.3.bp \(\chi_{630}(409, \cdot)\) n/a 192 2
630.3.br \(\chi_{630}(31, \cdot)\) n/a 128 2
630.3.bs \(\chi_{630}(47, \cdot)\) n/a 384 4
630.3.bu \(\chi_{630}(43, \cdot)\) n/a 288 4
630.3.bx \(\chi_{630}(37, \cdot)\) n/a 160 4
630.3.by \(\chi_{630}(247, \cdot)\) n/a 384 4
630.3.cb \(\chi_{630}(227, \cdot)\) n/a 384 4
630.3.cc \(\chi_{630}(17, \cdot)\) n/a 128 4
630.3.cf \(\chi_{630}(83, \cdot)\) n/a 384 4
630.3.ch \(\chi_{630}(67, \cdot)\) n/a 384 4

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(630))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(630)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 2}\)