Properties

Label 3150.3
Level 3150
Weight 3
Dimension 120828
Nonzero newspaces 60
Sturm bound 1555200
Trace bound 16

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Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1555200\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(3150))\).

Total New Old
Modular forms 523776 120828 402948
Cusp forms 513024 120828 392196
Eisenstein series 10752 0 10752

Trace form

\( 120828 q - 8 q^{2} - 4 q^{4} + 24 q^{6} + 22 q^{7} + 16 q^{8} + 136 q^{9} + O(q^{10}) \) \( 120828 q - 8 q^{2} - 4 q^{4} + 24 q^{6} + 22 q^{7} + 16 q^{8} + 136 q^{9} + 108 q^{10} + 302 q^{11} + 40 q^{12} + 196 q^{13} + 72 q^{14} - 48 q^{15} - 8 q^{16} - 54 q^{17} - 160 q^{18} - 34 q^{19} - 112 q^{20} - 90 q^{21} - 240 q^{22} + 34 q^{23} - 48 q^{24} + 252 q^{25} - 8 q^{26} - 60 q^{27} + 84 q^{28} - 340 q^{29} - 254 q^{31} - 48 q^{32} - 1004 q^{33} - 300 q^{34} - 776 q^{35} - 536 q^{36} - 6 q^{37} - 988 q^{38} - 1964 q^{39} + 24 q^{40} - 1316 q^{41} - 208 q^{42} - 444 q^{43} - 444 q^{44} + 160 q^{45} - 940 q^{46} + 274 q^{47} + 208 q^{48} - 66 q^{49} + 484 q^{50} + 1296 q^{51} - 56 q^{52} + 694 q^{53} + 1272 q^{54} - 944 q^{55} + 200 q^{56} + 1856 q^{57} + 112 q^{58} - 710 q^{59} - 896 q^{60} + 222 q^{61} - 2432 q^{62} - 1566 q^{63} + 128 q^{64} - 4276 q^{65} + 144 q^{66} - 1922 q^{67} - 988 q^{68} - 1028 q^{69} - 744 q^{70} - 488 q^{71} + 192 q^{72} - 1402 q^{73} + 384 q^{74} - 1088 q^{75} - 40 q^{76} - 268 q^{77} + 1440 q^{78} + 1070 q^{79} - 1520 q^{81} + 1712 q^{82} + 2764 q^{83} + 864 q^{84} + 4392 q^{85} - 384 q^{86} - 208 q^{87} - 1288 q^{88} - 422 q^{89} + 1280 q^{90} - 5244 q^{91} - 560 q^{92} - 2240 q^{93} - 2900 q^{94} - 2480 q^{95} - 512 q^{96} - 5412 q^{97} - 3648 q^{98} + 484 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(3150))\)

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
3150.3.c \(\chi_{3150}(449, \cdot)\) 3150.3.c.a 8 1
3150.3.c.b 8
3150.3.c.c 8
3150.3.c.d 16
3150.3.c.e 16
3150.3.c.f 16
3150.3.e \(\chi_{3150}(701, \cdot)\) 3150.3.e.a 4 1
3150.3.e.b 4
3150.3.e.c 4
3150.3.e.d 4
3150.3.e.e 4
3150.3.e.f 8
3150.3.e.g 8
3150.3.e.h 8
3150.3.e.i 8
3150.3.e.j 12
3150.3.e.k 12
3150.3.f \(\chi_{3150}(2701, \cdot)\) n/a 128 1
3150.3.h \(\chi_{3150}(2449, \cdot)\) n/a 120 1
3150.3.n \(\chi_{3150}(1007, \cdot)\) n/a 192 2
3150.3.o \(\chi_{3150}(757, \cdot)\) n/a 180 2
3150.3.r \(\chi_{3150}(851, \cdot)\) n/a 608 2
3150.3.t \(\chi_{3150}(599, \cdot)\) n/a 576 2
3150.3.w \(\chi_{3150}(451, \cdot)\) n/a 252 2
3150.3.x \(\chi_{3150}(1249, \cdot)\) n/a 576 2
3150.3.y \(\chi_{3150}(349, \cdot)\) n/a 576 2
3150.3.z \(\chi_{3150}(601, \cdot)\) n/a 608 2
3150.3.bc \(\chi_{3150}(1501, \cdot)\) n/a 608 2
3150.3.bd \(\chi_{3150}(199, \cdot)\) n/a 240 2
3150.3.be \(\chi_{3150}(2249, \cdot)\) n/a 192 2
3150.3.bh \(\chi_{3150}(1751, \cdot)\) n/a 456 2
3150.3.bi \(\chi_{3150}(401, \cdot)\) n/a 608 2
3150.3.bk \(\chi_{3150}(149, \cdot)\) n/a 576 2
3150.3.bn \(\chi_{3150}(1499, \cdot)\) n/a 432 2
3150.3.bo \(\chi_{3150}(2501, \cdot)\) n/a 200 2
3150.3.bq \(\chi_{3150}(1699, \cdot)\) n/a 576 2
3150.3.bs \(\chi_{3150}(1951, \cdot)\) n/a 608 2
3150.3.bt \(\chi_{3150}(559, \cdot)\) n/a 800 4
3150.3.bv \(\chi_{3150}(181, \cdot)\) n/a 800 4
3150.3.bw \(\chi_{3150}(71, \cdot)\) n/a 480 4
3150.3.by \(\chi_{3150}(1079, \cdot)\) n/a 480 4
3150.3.ca \(\chi_{3150}(1193, \cdot)\) n/a 1152 4
3150.3.cc \(\chi_{3150}(43, \cdot)\) n/a 864 4
3150.3.cf \(\chi_{3150}(793, \cdot)\) n/a 480 4
3150.3.cg \(\chi_{3150}(907, \cdot)\) n/a 1152 4
3150.3.cj \(\chi_{3150}(257, \cdot)\) n/a 1152 4
3150.3.ck \(\chi_{3150}(143, \cdot)\) n/a 384 4
3150.3.cn \(\chi_{3150}(293, \cdot)\) n/a 1152 4
3150.3.cp \(\chi_{3150}(193, \cdot)\) n/a 1152 4
3150.3.cv \(\chi_{3150}(127, \cdot)\) n/a 1200 8
3150.3.cw \(\chi_{3150}(377, \cdot)\) n/a 1280 8
3150.3.cy \(\chi_{3150}(31, \cdot)\) n/a 3840 8
3150.3.da \(\chi_{3150}(409, \cdot)\) n/a 3840 8
3150.3.dc \(\chi_{3150}(431, \cdot)\) n/a 1280 8
3150.3.dd \(\chi_{3150}(29, \cdot)\) n/a 2880 8
3150.3.dg \(\chi_{3150}(389, \cdot)\) n/a 3840 8
3150.3.di \(\chi_{3150}(11, \cdot)\) n/a 3840 8
3150.3.dj \(\chi_{3150}(281, \cdot)\) n/a 2880 8
3150.3.dm \(\chi_{3150}(179, \cdot)\) n/a 1280 8
3150.3.dn \(\chi_{3150}(19, \cdot)\) n/a 1600 8
3150.3.do \(\chi_{3150}(241, \cdot)\) n/a 3840 8
3150.3.dr \(\chi_{3150}(391, \cdot)\) n/a 3840 8
3150.3.ds \(\chi_{3150}(139, \cdot)\) n/a 3840 8
3150.3.dt \(\chi_{3150}(229, \cdot)\) n/a 3840 8
3150.3.du \(\chi_{3150}(271, \cdot)\) n/a 1600 8
3150.3.dx \(\chi_{3150}(569, \cdot)\) n/a 3840 8
3150.3.dz \(\chi_{3150}(191, \cdot)\) n/a 3840 8
3150.3.ea \(\chi_{3150}(67, \cdot)\) n/a 7680 16
3150.3.ec \(\chi_{3150}(83, \cdot)\) n/a 7680 16
3150.3.ef \(\chi_{3150}(17, \cdot)\) n/a 2560 16
3150.3.eg \(\chi_{3150}(227, \cdot)\) n/a 7680 16
3150.3.ej \(\chi_{3150}(247, \cdot)\) n/a 7680 16
3150.3.ek \(\chi_{3150}(37, \cdot)\) n/a 3200 16
3150.3.en \(\chi_{3150}(337, \cdot)\) n/a 5760 16
3150.3.ep \(\chi_{3150}(47, \cdot)\) n/a 7680 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(3150))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(3150)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1575))\)\(^{\oplus 2}\)