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Properties

Label 3075.2
Level 3075
Weight 2
Dimension 230382
Nonzero newspaces 98
Sturm bound 1344000
Trace bound 15

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Defining parameters

Level: \( N \) = \( 3075 = 3 \cdot 5^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 98 \)
Sturm bound: \(1344000\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3075))\).

Total New Old
Modular forms 340480 233582 106898
Cusp forms 331521 230382 101139
Eisenstein series 8959 3200 5759

Trace form

\( 230382 q + 2 q^{2} - 242 q^{3} - 470 q^{4} + 12 q^{5} - 374 q^{6} - 464 q^{7} + 42 q^{8} - 234 q^{9} + O(q^{10}) \) \( 230382 q + 2 q^{2} - 242 q^{3} - 470 q^{4} + 12 q^{5} - 374 q^{6} - 464 q^{7} + 42 q^{8} - 234 q^{9} - 572 q^{10} + 8 q^{11} - 222 q^{12} - 460 q^{13} + 48 q^{14} - 292 q^{15} - 774 q^{16} + 4 q^{17} - 258 q^{18} - 504 q^{19} - 72 q^{20} - 408 q^{21} - 552 q^{22} - 32 q^{23} - 362 q^{24} - 668 q^{25} + 12 q^{26} - 242 q^{27} - 608 q^{28} - 28 q^{29} - 348 q^{30} - 744 q^{31} + 106 q^{32} - 180 q^{33} - 380 q^{34} + 40 q^{35} - 298 q^{36} - 344 q^{37} + 64 q^{38} - 204 q^{39} - 644 q^{40} + 62 q^{41} - 492 q^{42} - 496 q^{43} + 144 q^{44} - 448 q^{45} - 784 q^{46} + 88 q^{47} - 254 q^{48} - 534 q^{49} - 212 q^{50} - 796 q^{51} - 576 q^{52} - 72 q^{53} - 450 q^{54} - 648 q^{55} - 376 q^{57} - 572 q^{58} - 56 q^{59} - 348 q^{60} - 732 q^{61} - 8 q^{62} - 204 q^{63} - 318 q^{64} + 116 q^{65} - 224 q^{66} - 176 q^{67} + 444 q^{68} + 28 q^{69} - 360 q^{70} + 272 q^{71} + 82 q^{72} - 132 q^{73} + 508 q^{74} - 92 q^{75} - 792 q^{76} + 352 q^{77} + 176 q^{78} - 160 q^{79} + 308 q^{80} - 258 q^{81} + 6 q^{82} + 216 q^{83} + 232 q^{84} - 716 q^{85} + 408 q^{86} - 152 q^{87} - 248 q^{88} + 16 q^{89} - 272 q^{90} - 544 q^{91} + 176 q^{92} - 316 q^{93} - 504 q^{94} - 112 q^{95} - 286 q^{96} - 676 q^{97} + 10 q^{98} - 252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3075))\)

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
3075.2.a \(\chi_{3075}(1, \cdot)\) 3075.2.a.a 1 1
3075.2.a.b 1
3075.2.a.c 1
3075.2.a.d 1
3075.2.a.e 1
3075.2.a.f 1
3075.2.a.g 1
3075.2.a.h 1
3075.2.a.i 1
3075.2.a.j 1
3075.2.a.k 1
3075.2.a.l 1
3075.2.a.m 1
3075.2.a.n 1
3075.2.a.o 2
3075.2.a.p 2
3075.2.a.q 2
3075.2.a.r 2
3075.2.a.s 3
3075.2.a.t 3
3075.2.a.u 3
3075.2.a.v 4
3075.2.a.w 5
3075.2.a.x 6
3075.2.a.y 7
3075.2.a.z 7
3075.2.a.ba 8
3075.2.a.bb 9
3075.2.a.bc 9
3075.2.a.bd 10
3075.2.a.be 10
3075.2.a.bf 10
3075.2.a.bg 10
3075.2.b \(\chi_{3075}(124, \cdot)\) n/a 120 1
3075.2.e \(\chi_{3075}(1024, \cdot)\) n/a 128 1
3075.2.f \(\chi_{3075}(901, \cdot)\) n/a 132 1
3075.2.j \(\chi_{3075}(1426, \cdot)\) n/a 268 2
3075.2.k \(\chi_{3075}(893, \cdot)\) n/a 496 2
3075.2.m \(\chi_{3075}(1682, \cdot)\) n/a 480 2
3075.2.p \(\chi_{3075}(368, \cdot)\) n/a 496 2
3075.2.r \(\chi_{3075}(32, \cdot)\) n/a 496 2
3075.2.s \(\chi_{3075}(1549, \cdot)\) n/a 248 2
3075.2.u \(\chi_{3075}(406, \cdot)\) n/a 848 4
3075.2.v \(\chi_{3075}(1576, \cdot)\) n/a 528 4
3075.2.w \(\chi_{3075}(1246, \cdot)\) n/a 848 4
3075.2.x \(\chi_{3075}(16, \cdot)\) n/a 848 4
3075.2.y \(\chi_{3075}(616, \cdot)\) n/a 800 4
3075.2.z \(\chi_{3075}(346, \cdot)\) n/a 848 4
3075.2.bb \(\chi_{3075}(232, \cdot)\) n/a 504 4
3075.2.bc \(\chi_{3075}(899, \cdot)\) n/a 992 4
3075.2.bf \(\chi_{3075}(776, \cdot)\) n/a 1040 4
3075.2.bg \(\chi_{3075}(793, \cdot)\) n/a 504 4
3075.2.bj \(\chi_{3075}(394, \cdot)\) n/a 832 4
3075.2.bk \(\chi_{3075}(1369, \cdot)\) n/a 832 4
3075.2.bn \(\chi_{3075}(286, \cdot)\) n/a 848 4
3075.2.bt \(\chi_{3075}(31, \cdot)\) n/a 848 4
3075.2.bv \(\chi_{3075}(271, \cdot)\) n/a 848 4
3075.2.bx \(\chi_{3075}(1501, \cdot)\) n/a 528 4
3075.2.bz \(\chi_{3075}(646, \cdot)\) n/a 848 4
3075.2.cc \(\chi_{3075}(739, \cdot)\) n/a 800 4
3075.2.cd \(\chi_{3075}(4, \cdot)\) n/a 832 4
3075.2.cf \(\chi_{3075}(1624, \cdot)\) n/a 512 4
3075.2.ch \(\chi_{3075}(154, \cdot)\) n/a 832 4
3075.2.cj \(\chi_{3075}(1294, \cdot)\) n/a 832 4
3075.2.cm \(\chi_{3075}(469, \cdot)\) n/a 832 4
3075.2.co \(\chi_{3075}(139, \cdot)\) n/a 832 4
3075.2.cq \(\chi_{3075}(1699, \cdot)\) n/a 512 4
3075.2.cs \(\chi_{3075}(529, \cdot)\) n/a 832 4
3075.2.ct \(\chi_{3075}(409, \cdot)\) n/a 832 4
3075.2.cw \(\chi_{3075}(1171, \cdot)\) n/a 848 4
3075.2.cy \(\chi_{3075}(121, \cdot)\) n/a 1664 8
3075.2.da \(\chi_{3075}(184, \cdot)\) n/a 1696 8
3075.2.df \(\chi_{3075}(169, \cdot)\) n/a 1696 8
3075.2.dg \(\chi_{3075}(49, \cdot)\) n/a 992 8
3075.2.dh \(\chi_{3075}(244, \cdot)\) n/a 1696 8
3075.2.di \(\chi_{3075}(214, \cdot)\) n/a 1696 8
3075.2.dl \(\chi_{3075}(203, \cdot)\) n/a 3328 8
3075.2.dm \(\chi_{3075}(1253, \cdot)\) n/a 3328 8
3075.2.dp \(\chi_{3075}(428, \cdot)\) n/a 3328 8
3075.2.dq \(\chi_{3075}(377, \cdot)\) n/a 3328 8
3075.2.dt \(\chi_{3075}(278, \cdot)\) n/a 3328 8
3075.2.du \(\chi_{3075}(77, \cdot)\) n/a 3328 8
3075.2.dw \(\chi_{3075}(197, \cdot)\) n/a 3328 8
3075.2.dx \(\chi_{3075}(2, \cdot)\) n/a 3328 8
3075.2.dy \(\chi_{3075}(743, \cdot)\) n/a 1984 8
3075.2.ec \(\chi_{3075}(92, \cdot)\) n/a 3328 8
3075.2.ee \(\chi_{3075}(107, \cdot)\) n/a 1984 8
3075.2.eg \(\chi_{3075}(638, \cdot)\) n/a 3328 8
3075.2.eh \(\chi_{3075}(113, \cdot)\) n/a 3328 8
3075.2.ei \(\chi_{3075}(122, \cdot)\) n/a 3328 8
3075.2.ep \(\chi_{3075}(83, \cdot)\) n/a 3200 8
3075.2.eq \(\chi_{3075}(338, \cdot)\) n/a 3328 8
3075.2.er \(\chi_{3075}(98, \cdot)\) n/a 3328 8
3075.2.et \(\chi_{3075}(182, \cdot)\) n/a 1984 8
3075.2.ev \(\chi_{3075}(23, \cdot)\) n/a 3328 8
3075.2.ez \(\chi_{3075}(143, \cdot)\) n/a 1984 8
3075.2.fa \(\chi_{3075}(62, \cdot)\) n/a 3328 8
3075.2.fb \(\chi_{3075}(677, \cdot)\) n/a 3328 8
3075.2.fd \(\chi_{3075}(323, \cdot)\) n/a 3328 8
3075.2.fe \(\chi_{3075}(173, \cdot)\) n/a 3328 8
3075.2.fh \(\chi_{3075}(91, \cdot)\) n/a 1664 8
3075.2.fi \(\chi_{3075}(226, \cdot)\) n/a 1072 8
3075.2.fj \(\chi_{3075}(61, \cdot)\) n/a 1664 8
3075.2.fk \(\chi_{3075}(541, \cdot)\) n/a 1664 8
3075.2.fp \(\chi_{3075}(46, \cdot)\) n/a 1664 8
3075.2.fr \(\chi_{3075}(664, \cdot)\) n/a 1696 8
3075.2.fs \(\chi_{3075}(28, \cdot)\) n/a 3360 16
3075.2.fu \(\chi_{3075}(178, \cdot)\) n/a 3360 16
3075.2.fz \(\chi_{3075}(112, \cdot)\) n/a 3360 16
3075.2.ga \(\chi_{3075}(7, \cdot)\) n/a 2016 16
3075.2.gb \(\chi_{3075}(58, \cdot)\) n/a 3360 16
3075.2.gc \(\chi_{3075}(88, \cdot)\) n/a 3360 16
3075.2.gf \(\chi_{3075}(404, \cdot)\) n/a 6656 16
3075.2.gg \(\chi_{3075}(11, \cdot)\) n/a 6656 16
3075.2.gj \(\chi_{3075}(281, \cdot)\) n/a 6656 16
3075.2.gk \(\chi_{3075}(26, \cdot)\) n/a 4160 16
3075.2.gl \(\chi_{3075}(161, \cdot)\) n/a 6656 16
3075.2.gm \(\chi_{3075}(56, \cdot)\) n/a 6656 16
3075.2.gr \(\chi_{3075}(116, \cdot)\) n/a 6656 16
3075.2.gs \(\chi_{3075}(29, \cdot)\) n/a 6656 16
3075.2.gx \(\chi_{3075}(104, \cdot)\) n/a 6656 16
3075.2.gy \(\chi_{3075}(14, \cdot)\) n/a 6656 16
3075.2.gz \(\chi_{3075}(89, \cdot)\) n/a 6656 16
3075.2.ha \(\chi_{3075}(149, \cdot)\) n/a 3968 16
3075.2.hd \(\chi_{3075}(22, \cdot)\) n/a 3360 16
3075.2.he \(\chi_{3075}(13, \cdot)\) n/a 3360 16
3075.2.hf \(\chi_{3075}(97, \cdot)\) n/a 3360 16
3075.2.hg \(\chi_{3075}(193, \cdot)\) n/a 2016 16
3075.2.hl \(\chi_{3075}(208, \cdot)\) n/a 3360 16
3075.2.hn \(\chi_{3075}(52, \cdot)\) n/a 3360 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3075))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3075)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(615))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1025))\)\(^{\oplus 2}\)