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

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

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 the 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

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