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Properties

Label 2952.2
Level 2952
Weight 2
Dimension 106900
Nonzero newspaces 48
Sturm bound 967680
Trace bound 16

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Defining parameters

Level: \( N \) = \( 2952 = 2^{3} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(967680\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2952))\).

Total New Old
Modular forms 245760 108304 137456
Cusp forms 238081 106900 131181
Eisenstein series 7679 1404 6275

Trace form

\( 106900 q - 116 q^{2} - 154 q^{3} - 116 q^{4} - 8 q^{5} - 144 q^{6} - 116 q^{7} - 92 q^{8} - 302 q^{9} + O(q^{10}) \) \( 106900 q - 116 q^{2} - 154 q^{3} - 116 q^{4} - 8 q^{5} - 144 q^{6} - 116 q^{7} - 92 q^{8} - 302 q^{9} - 312 q^{10} - 86 q^{11} - 132 q^{12} + 4 q^{13} - 92 q^{14} - 112 q^{15} - 100 q^{16} - 200 q^{17} - 160 q^{18} - 316 q^{19} - 140 q^{20} + 24 q^{21} - 148 q^{22} - 84 q^{23} - 208 q^{24} - 224 q^{25} - 176 q^{26} - 160 q^{27} - 376 q^{28} - 12 q^{29} - 252 q^{30} - 88 q^{31} - 196 q^{32} - 306 q^{33} - 92 q^{34} - 192 q^{35} - 260 q^{36} - 12 q^{37} - 196 q^{38} - 232 q^{39} - 140 q^{40} - 235 q^{41} - 420 q^{42} - 170 q^{43} - 204 q^{44} - 4 q^{45} - 392 q^{46} - 204 q^{47} - 200 q^{48} - 136 q^{49} - 176 q^{50} - 178 q^{51} - 68 q^{52} + 28 q^{53} - 136 q^{54} - 328 q^{55} - 56 q^{56} - 262 q^{57} - 100 q^{58} - 122 q^{59} - 28 q^{60} + 16 q^{61} + 8 q^{62} - 224 q^{63} - 320 q^{64} - 182 q^{65} + 48 q^{66} - 130 q^{67} + 48 q^{68} - 44 q^{69} - 28 q^{70} - 216 q^{71} + 44 q^{72} - 752 q^{73} + 100 q^{74} - 258 q^{75} - 52 q^{76} - 104 q^{77} - 12 q^{78} - 192 q^{79} + 72 q^{80} - 342 q^{81} - 380 q^{82} - 384 q^{83} - 32 q^{84} - 186 q^{85} - 20 q^{86} - 196 q^{87} - 148 q^{88} - 364 q^{89} - 132 q^{90} - 568 q^{91} - 228 q^{92} + 20 q^{93} - 168 q^{94} - 328 q^{95} - 256 q^{96} - 422 q^{97} - 312 q^{98} - 220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2952))\)

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
2952.2.a \(\chi_{2952}(1, \cdot)\) 2952.2.a.a 1 1
2952.2.a.b 1
2952.2.a.c 1
2952.2.a.d 1
2952.2.a.e 1
2952.2.a.f 1
2952.2.a.g 1
2952.2.a.h 1
2952.2.a.i 2
2952.2.a.j 2
2952.2.a.k 3
2952.2.a.l 3
2952.2.a.m 3
2952.2.a.n 3
2952.2.a.o 3
2952.2.a.p 4
2952.2.a.q 4
2952.2.a.r 5
2952.2.a.s 5
2952.2.a.t 5
2952.2.d \(\chi_{2952}(575, \cdot)\) None 0 1
2952.2.e \(\chi_{2952}(901, \cdot)\) n/a 208 1
2952.2.f \(\chi_{2952}(1477, \cdot)\) n/a 200 1
2952.2.g \(\chi_{2952}(2951, \cdot)\) None 0 1
2952.2.j \(\chi_{2952}(2377, \cdot)\) 2952.2.j.a 2 1
2952.2.j.b 4
2952.2.j.c 6
2952.2.j.d 8
2952.2.j.e 10
2952.2.j.f 10
2952.2.j.g 12
2952.2.k \(\chi_{2952}(2051, \cdot)\) n/a 160 1
2952.2.p \(\chi_{2952}(1475, \cdot)\) n/a 168 1
2952.2.q \(\chi_{2952}(985, \cdot)\) n/a 240 2
2952.2.t \(\chi_{2952}(1403, \cdot)\) n/a 336 2
2952.2.u \(\chi_{2952}(73, \cdot)\) n/a 106 2
2952.2.x \(\chi_{2952}(647, \cdot)\) None 0 2
2952.2.y \(\chi_{2952}(829, \cdot)\) n/a 416 2
2952.2.z \(\chi_{2952}(1369, \cdot)\) n/a 208 4
2952.2.ba \(\chi_{2952}(491, \cdot)\) n/a 1000 2
2952.2.bf \(\chi_{2952}(409, \cdot)\) n/a 252 2
2952.2.bg \(\chi_{2952}(83, \cdot)\) n/a 960 2
2952.2.bj \(\chi_{2952}(493, \cdot)\) n/a 960 2
2952.2.bk \(\chi_{2952}(983, \cdot)\) None 0 2
2952.2.bl \(\chi_{2952}(1559, \cdot)\) None 0 2
2952.2.bm \(\chi_{2952}(1885, \cdot)\) n/a 1000 2
2952.2.bt \(\chi_{2952}(413, \cdot)\) n/a 672 4
2952.2.bu \(\chi_{2952}(161, \cdot)\) n/a 168 4
2952.2.bv \(\chi_{2952}(1315, \cdot)\) n/a 832 4
2952.2.bw \(\chi_{2952}(55, \cdot)\) None 0 4
2952.2.bx \(\chi_{2952}(107, \cdot)\) n/a 672 4
2952.2.cc \(\chi_{2952}(467, \cdot)\) n/a 672 4
2952.2.cd \(\chi_{2952}(433, \cdot)\) n/a 208 4
2952.2.cg \(\chi_{2952}(359, \cdot)\) None 0 4
2952.2.ch \(\chi_{2952}(37, \cdot)\) n/a 832 4
2952.2.ci \(\chi_{2952}(1261, \cdot)\) n/a 832 4
2952.2.cj \(\chi_{2952}(215, \cdot)\) None 0 4
2952.2.cm \(\chi_{2952}(565, \cdot)\) n/a 2000 4
2952.2.cn \(\chi_{2952}(911, \cdot)\) None 0 4
2952.2.cq \(\chi_{2952}(337, \cdot)\) n/a 504 4
2952.2.cr \(\chi_{2952}(155, \cdot)\) n/a 2000 4
2952.2.cu \(\chi_{2952}(385, \cdot)\) n/a 1008 8
2952.2.cv \(\chi_{2952}(541, \cdot)\) n/a 1664 8
2952.2.cw \(\chi_{2952}(143, \cdot)\) None 0 8
2952.2.cz \(\chi_{2952}(289, \cdot)\) n/a 424 8
2952.2.da \(\chi_{2952}(251, \cdot)\) n/a 1344 8
2952.2.dd \(\chi_{2952}(331, \cdot)\) n/a 4000 8
2952.2.de \(\chi_{2952}(79, \cdot)\) None 0 8
2952.2.df \(\chi_{2952}(437, \cdot)\) n/a 4000 8
2952.2.dg \(\chi_{2952}(137, \cdot)\) n/a 1008 8
2952.2.dn \(\chi_{2952}(277, \cdot)\) n/a 4000 8
2952.2.do \(\chi_{2952}(119, \cdot)\) None 0 8
2952.2.dp \(\chi_{2952}(23, \cdot)\) None 0 8
2952.2.dq \(\chi_{2952}(133, \cdot)\) n/a 4000 8
2952.2.dt \(\chi_{2952}(59, \cdot)\) n/a 4000 8
2952.2.du \(\chi_{2952}(25, \cdot)\) n/a 1008 8
2952.2.dz \(\chi_{2952}(515, \cdot)\) n/a 4000 8
2952.2.ea \(\chi_{2952}(199, \cdot)\) None 0 16
2952.2.eb \(\chi_{2952}(19, \cdot)\) n/a 3328 16
2952.2.ec \(\chi_{2952}(17, \cdot)\) n/a 672 16
2952.2.ed \(\chi_{2952}(53, \cdot)\) n/a 2688 16
2952.2.ek \(\chi_{2952}(131, \cdot)\) n/a 8000 16
2952.2.el \(\chi_{2952}(49, \cdot)\) n/a 2016 16
2952.2.eo \(\chi_{2952}(623, \cdot)\) None 0 16
2952.2.ep \(\chi_{2952}(61, \cdot)\) n/a 8000 16
2952.2.eu \(\chi_{2952}(65, \cdot)\) n/a 4032 32
2952.2.ev \(\chi_{2952}(29, \cdot)\) n/a 16000 32
2952.2.ew \(\chi_{2952}(7, \cdot)\) None 0 32
2952.2.ex \(\chi_{2952}(67, \cdot)\) n/a 16000 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2952))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2952)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(369))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(738))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(984))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2952))\)\(^{\oplus 1}\)