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Properties

Label 2205.2
Level 2205
Weight 2
Dimension 116619
Nonzero newspaces 60
Sturm bound 677376
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(677376\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2205))\).

Total New Old
Modular forms 173184 119237 53947
Cusp forms 165505 116619 48886
Eisenstein series 7679 2618 5061

Trace form

\( 116619 q - 97 q^{2} - 128 q^{3} - 117 q^{4} - 150 q^{5} - 376 q^{6} - 116 q^{7} - 201 q^{8} - 124 q^{9} + O(q^{10}) \) \( 116619 q - 97 q^{2} - 128 q^{3} - 117 q^{4} - 150 q^{5} - 376 q^{6} - 116 q^{7} - 201 q^{8} - 124 q^{9} - 450 q^{10} - 310 q^{11} - 64 q^{12} - 120 q^{13} - 96 q^{14} - 296 q^{15} - 229 q^{16} - 4 q^{17} - 8 q^{18} - 246 q^{19} - 20 q^{20} - 396 q^{21} - 82 q^{22} - 18 q^{23} + 60 q^{24} - 138 q^{25} - 76 q^{26} - 32 q^{27} - 288 q^{28} - 92 q^{29} - 64 q^{30} - 234 q^{31} + 259 q^{32} - 16 q^{33} + 128 q^{34} - 93 q^{35} - 440 q^{36} - 88 q^{37} + 326 q^{38} - 8 q^{39} + 226 q^{40} + 88 q^{41} - 12 q^{42} - 22 q^{43} + 490 q^{44} - 112 q^{45} - 346 q^{46} + 86 q^{47} - 208 q^{48} + 84 q^{49} - 331 q^{50} - 376 q^{51} + 384 q^{52} - 136 q^{53} - 244 q^{54} - 282 q^{55} - 180 q^{56} - 392 q^{57} + 188 q^{58} - 214 q^{59} - 364 q^{60} - 54 q^{61} - 294 q^{62} - 312 q^{63} - 297 q^{64} - 55 q^{65} - 440 q^{66} + 114 q^{67} - 344 q^{68} - 156 q^{69} + 51 q^{70} - 302 q^{71} - 312 q^{72} + 84 q^{73} + 256 q^{74} - 164 q^{75} + 242 q^{76} + 54 q^{77} - 112 q^{78} + 270 q^{79} - 89 q^{80} - 64 q^{81} + 330 q^{82} + 402 q^{83} + 15 q^{85} + 416 q^{86} + 52 q^{87} + 480 q^{88} + 216 q^{89} - 344 q^{90} - 818 q^{91} - 228 q^{92} - 60 q^{93} + 104 q^{94} - 337 q^{95} - 536 q^{96} - 50 q^{97} + 312 q^{98} - 404 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2205))\)

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
2205.2.a \(\chi_{2205}(1, \cdot)\) 2205.2.a.a 1 1
2205.2.a.b 1
2205.2.a.c 1
2205.2.a.d 1
2205.2.a.e 1
2205.2.a.f 1
2205.2.a.g 1
2205.2.a.h 1
2205.2.a.i 1
2205.2.a.j 1
2205.2.a.k 1
2205.2.a.l 1
2205.2.a.m 1
2205.2.a.n 2
2205.2.a.o 2
2205.2.a.p 2
2205.2.a.q 2
2205.2.a.r 2
2205.2.a.s 2
2205.2.a.t 2
2205.2.a.u 2
2205.2.a.v 2
2205.2.a.w 2
2205.2.a.x 2
2205.2.a.y 2
2205.2.a.z 2
2205.2.a.ba 2
2205.2.a.bb 3
2205.2.a.bc 3
2205.2.a.bd 3
2205.2.a.be 3
2205.2.a.bf 4
2205.2.a.bg 4
2205.2.a.bh 4
2205.2.a.bi 4
2205.2.b \(\chi_{2205}(881, \cdot)\) 2205.2.b.a 12 1
2205.2.b.b 12
2205.2.b.c 16
2205.2.b.d 16
2205.2.d \(\chi_{2205}(1324, \cdot)\) 2205.2.d.a 2 1
2205.2.d.b 2
2205.2.d.c 2
2205.2.d.d 2
2205.2.d.e 2
2205.2.d.f 2
2205.2.d.g 2
2205.2.d.h 2
2205.2.d.i 4
2205.2.d.j 4
2205.2.d.k 4
2205.2.d.l 6
2205.2.d.m 8
2205.2.d.n 8
2205.2.d.o 8
2205.2.d.p 8
2205.2.d.q 8
2205.2.d.r 8
2205.2.d.s 8
2205.2.d.t 8
2205.2.g \(\chi_{2205}(2204, \cdot)\) 2205.2.g.a 8 1
2205.2.g.b 24
2205.2.g.c 48
2205.2.i \(\chi_{2205}(736, \cdot)\) n/a 328 2
2205.2.j \(\chi_{2205}(226, \cdot)\) n/a 132 2
2205.2.k \(\chi_{2205}(961, \cdot)\) n/a 320 2
2205.2.l \(\chi_{2205}(1096, \cdot)\) n/a 320 2
2205.2.m \(\chi_{2205}(197, \cdot)\) n/a 164 2
2205.2.p \(\chi_{2205}(1567, \cdot)\) n/a 192 2
2205.2.r \(\chi_{2205}(214, \cdot)\) n/a 464 2
2205.2.t \(\chi_{2205}(1391, \cdot)\) n/a 320 2
2205.2.u \(\chi_{2205}(374, \cdot)\) n/a 464 2
2205.2.z \(\chi_{2205}(734, \cdot)\) n/a 464 2
2205.2.bb \(\chi_{2205}(1844, \cdot)\) n/a 160 2
2205.2.be \(\chi_{2205}(1256, \cdot)\) n/a 320 2
2205.2.bf \(\chi_{2205}(1549, \cdot)\) n/a 192 2
2205.2.bh \(\chi_{2205}(589, \cdot)\) n/a 472 2
2205.2.bj \(\chi_{2205}(521, \cdot)\) n/a 104 2
2205.2.bl \(\chi_{2205}(146, \cdot)\) n/a 320 2
2205.2.bo \(\chi_{2205}(79, \cdot)\) n/a 464 2
2205.2.bq \(\chi_{2205}(509, \cdot)\) n/a 464 2
2205.2.bs \(\chi_{2205}(316, \cdot)\) n/a 552 6
2205.2.bt \(\chi_{2205}(178, \cdot)\) n/a 928 4
2205.2.bw \(\chi_{2205}(263, \cdot)\) n/a 928 4
2205.2.by \(\chi_{2205}(128, \cdot)\) n/a 928 4
2205.2.ca \(\chi_{2205}(1207, \cdot)\) n/a 384 4
2205.2.cc \(\chi_{2205}(97, \cdot)\) n/a 928 4
2205.2.cd \(\chi_{2205}(932, \cdot)\) n/a 944 4
2205.2.cf \(\chi_{2205}(422, \cdot)\) n/a 320 4
2205.2.ch \(\chi_{2205}(313, \cdot)\) n/a 928 4
2205.2.ck \(\chi_{2205}(314, \cdot)\) n/a 672 6
2205.2.cn \(\chi_{2205}(64, \cdot)\) n/a 828 6
2205.2.cp \(\chi_{2205}(251, \cdot)\) n/a 432 6
2205.2.cq \(\chi_{2205}(121, \cdot)\) n/a 2688 12
2205.2.cr \(\chi_{2205}(16, \cdot)\) n/a 2688 12
2205.2.cs \(\chi_{2205}(46, \cdot)\) n/a 1128 12
2205.2.ct \(\chi_{2205}(106, \cdot)\) n/a 2688 12
2205.2.cv \(\chi_{2205}(118, \cdot)\) n/a 1656 12
2205.2.cw \(\chi_{2205}(8, \cdot)\) n/a 1344 12
2205.2.cz \(\chi_{2205}(164, \cdot)\) n/a 3984 12
2205.2.db \(\chi_{2205}(4, \cdot)\) n/a 3984 12
2205.2.de \(\chi_{2205}(41, \cdot)\) n/a 2688 12
2205.2.dg \(\chi_{2205}(26, \cdot)\) n/a 912 12
2205.2.di \(\chi_{2205}(169, \cdot)\) n/a 3984 12
2205.2.dk \(\chi_{2205}(109, \cdot)\) n/a 1656 12
2205.2.dl \(\chi_{2205}(236, \cdot)\) n/a 2688 12
2205.2.do \(\chi_{2205}(89, \cdot)\) n/a 1344 12
2205.2.dq \(\chi_{2205}(104, \cdot)\) n/a 3984 12
2205.2.dv \(\chi_{2205}(59, \cdot)\) n/a 3984 12
2205.2.dw \(\chi_{2205}(101, \cdot)\) n/a 2688 12
2205.2.dy \(\chi_{2205}(184, \cdot)\) n/a 3984 12
2205.2.ea \(\chi_{2205}(157, \cdot)\) n/a 7968 24
2205.2.ec \(\chi_{2205}(92, \cdot)\) n/a 7968 24
2205.2.ee \(\chi_{2205}(53, \cdot)\) n/a 2688 24
2205.2.eh \(\chi_{2205}(73, \cdot)\) n/a 3312 24
2205.2.ej \(\chi_{2205}(13, \cdot)\) n/a 7968 24
2205.2.el \(\chi_{2205}(2, \cdot)\) n/a 7968 24
2205.2.en \(\chi_{2205}(23, \cdot)\) n/a 7968 24
2205.2.eo \(\chi_{2205}(52, \cdot)\) n/a 7968 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2205))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2205)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 2}\)