Properties

Label 2325.2
Level 2325
Weight 2
Dimension 131252
Nonzero newspaces 84
Sturm bound 768000
Trace bound 14

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Defining parameters

Level: \( N \) = \( 2325 = 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(768000\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2325))\).

Total New Old
Modular forms 195360 133632 61728
Cusp forms 188641 131252 57389
Eisenstein series 6719 2380 4339

Trace form

\( 131252 q + 2 q^{2} - 177 q^{3} - 340 q^{4} + 12 q^{5} - 269 q^{6} - 334 q^{7} + 42 q^{8} - 169 q^{9} + O(q^{10}) \) \( 131252 q + 2 q^{2} - 177 q^{3} - 340 q^{4} + 12 q^{5} - 269 q^{6} - 334 q^{7} + 42 q^{8} - 169 q^{9} - 412 q^{10} + 8 q^{11} - 157 q^{12} - 330 q^{13} + 48 q^{14} - 212 q^{15} - 564 q^{16} + 4 q^{17} - 193 q^{18} - 374 q^{19} - 72 q^{20} - 298 q^{21} - 362 q^{22} - 2 q^{23} - 237 q^{24} - 508 q^{25} + 72 q^{26} - 177 q^{27} - 318 q^{28} + 32 q^{29} - 268 q^{30} - 542 q^{31} + 146 q^{32} - 145 q^{33} - 230 q^{34} + 40 q^{35} - 313 q^{36} - 244 q^{37} + 44 q^{38} - 184 q^{39} - 484 q^{40} + 74 q^{41} - 297 q^{42} - 396 q^{43} - 96 q^{44} - 368 q^{45} - 654 q^{46} - 32 q^{47} - 284 q^{48} - 424 q^{49} - 212 q^{50} - 561 q^{51} - 436 q^{52} - 52 q^{53} - 260 q^{54} - 488 q^{55} + 270 q^{56} - 221 q^{57} - 232 q^{58} + 4 q^{59} - 268 q^{60} - 312 q^{61} + 176 q^{62} - 214 q^{63} + 52 q^{64} + 116 q^{65} + 26 q^{66} - 106 q^{67} + 454 q^{68} + 103 q^{69} - 200 q^{70} + 232 q^{71} + 312 q^{72} - 102 q^{73} + 418 q^{74} - 12 q^{75} - 832 q^{76} + 252 q^{77} - 4 q^{78} - 190 q^{79} + 308 q^{80} - 253 q^{81} - 298 q^{82} + 56 q^{83} - 163 q^{84} - 556 q^{85} + 8 q^{86} - 227 q^{87} - 518 q^{88} - 144 q^{89} - 192 q^{90} - 654 q^{91} - 64 q^{92} - 383 q^{93} - 1124 q^{94} - 112 q^{95} - 516 q^{96} - 706 q^{97} - 190 q^{98} - 262 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2325))\)

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
2325.2.a \(\chi_{2325}(1, \cdot)\) 2325.2.a.a 1 1
2325.2.a.b 1
2325.2.a.c 1
2325.2.a.d 1
2325.2.a.e 1
2325.2.a.f 1
2325.2.a.g 1
2325.2.a.h 1
2325.2.a.i 1
2325.2.a.j 1
2325.2.a.k 1
2325.2.a.l 1
2325.2.a.m 2
2325.2.a.n 2
2325.2.a.o 2
2325.2.a.p 3
2325.2.a.q 3
2325.2.a.r 3
2325.2.a.s 3
2325.2.a.t 3
2325.2.a.u 3
2325.2.a.v 4
2325.2.a.w 5
2325.2.a.x 5
2325.2.a.y 6
2325.2.a.z 6
2325.2.a.ba 6
2325.2.a.bb 6
2325.2.a.bc 11
2325.2.a.bd 11
2325.2.c \(\chi_{2325}(1024, \cdot)\) 2325.2.c.a 2 1
2325.2.c.b 2
2325.2.c.c 2
2325.2.c.d 2
2325.2.c.e 2
2325.2.c.f 2
2325.2.c.g 2
2325.2.c.h 4
2325.2.c.i 4
2325.2.c.j 4
2325.2.c.k 6
2325.2.c.l 6
2325.2.c.m 6
2325.2.c.n 6
2325.2.c.o 6
2325.2.c.p 8
2325.2.c.q 12
2325.2.c.r 12
2325.2.e \(\chi_{2325}(1301, \cdot)\) n/a 196 1
2325.2.g \(\chi_{2325}(2324, \cdot)\) n/a 188 1
2325.2.i \(\chi_{2325}(676, \cdot)\) n/a 202 2
2325.2.j \(\chi_{2325}(2107, \cdot)\) n/a 192 2
2325.2.k \(\chi_{2325}(32, \cdot)\) n/a 360 2
2325.2.n \(\chi_{2325}(376, \cdot)\) n/a 408 4
2325.2.o \(\chi_{2325}(721, \cdot)\) n/a 640 4
2325.2.p \(\chi_{2325}(946, \cdot)\) n/a 640 4
2325.2.q \(\chi_{2325}(481, \cdot)\) n/a 640 4
2325.2.r \(\chi_{2325}(466, \cdot)\) n/a 592 4
2325.2.s \(\chi_{2325}(16, \cdot)\) n/a 640 4
2325.2.t \(\chi_{2325}(26, \cdot)\) n/a 394 2
2325.2.v \(\chi_{2325}(1699, \cdot)\) n/a 192 2
2325.2.y \(\chi_{2325}(1049, \cdot)\) n/a 376 2
2325.2.ba \(\chi_{2325}(581, \cdot)\) n/a 1264 4
2325.2.bc \(\chi_{2325}(4, \cdot)\) n/a 640 4
2325.2.be \(\chi_{2325}(464, \cdot)\) n/a 1264 4
2325.2.bl \(\chi_{2325}(89, \cdot)\) n/a 1264 4
2325.2.bm \(\chi_{2325}(449, \cdot)\) n/a 752 4
2325.2.bn \(\chi_{2325}(914, \cdot)\) n/a 1264 4
2325.2.br \(\chi_{2325}(29, \cdot)\) n/a 1264 4
2325.2.bt \(\chi_{2325}(94, \cdot)\) n/a 608 4
2325.2.bw \(\chi_{2325}(116, \cdot)\) n/a 1264 4
2325.2.bx \(\chi_{2325}(866, \cdot)\) n/a 1264 4
2325.2.by \(\chi_{2325}(401, \cdot)\) n/a 784 4
2325.2.cc \(\chi_{2325}(356, \cdot)\) n/a 1264 4
2325.2.ce \(\chi_{2325}(469, \cdot)\) n/a 640 4
2325.2.cf \(\chi_{2325}(349, \cdot)\) n/a 384 4
2325.2.cg \(\chi_{2325}(994, \cdot)\) n/a 640 4
2325.2.ck \(\chi_{2325}(529, \cdot)\) n/a 640 4
2325.2.cl \(\chi_{2325}(371, \cdot)\) n/a 1264 4
2325.2.co \(\chi_{2325}(554, \cdot)\) n/a 1264 4
2325.2.cs \(\chi_{2325}(707, \cdot)\) n/a 752 4
2325.2.ct \(\chi_{2325}(832, \cdot)\) n/a 384 4
2325.2.cu \(\chi_{2325}(211, \cdot)\) n/a 1280 8
2325.2.cv \(\chi_{2325}(196, \cdot)\) n/a 1280 8
2325.2.cw \(\chi_{2325}(121, \cdot)\) n/a 1280 8
2325.2.cx \(\chi_{2325}(391, \cdot)\) n/a 1280 8
2325.2.cy \(\chi_{2325}(76, \cdot)\) n/a 808 8
2325.2.cz \(\chi_{2325}(661, \cdot)\) n/a 1280 8
2325.2.dc \(\chi_{2325}(2, \cdot)\) n/a 2528 8
2325.2.dd \(\chi_{2325}(277, \cdot)\) n/a 1280 8
2325.2.de \(\chi_{2325}(233, \cdot)\) n/a 2528 8
2325.2.df \(\chi_{2325}(337, \cdot)\) n/a 1280 8
2325.2.do \(\chi_{2325}(523, \cdot)\) n/a 1280 8
2325.2.dp \(\chi_{2325}(188, \cdot)\) n/a 2528 8
2325.2.dq \(\chi_{2325}(497, \cdot)\) n/a 2400 8
2325.2.dr \(\chi_{2325}(407, \cdot)\) n/a 1504 8
2325.2.ds \(\chi_{2325}(247, \cdot)\) n/a 1280 8
2325.2.dt \(\chi_{2325}(232, \cdot)\) n/a 768 8
2325.2.du \(\chi_{2325}(58, \cdot)\) n/a 1280 8
2325.2.dv \(\chi_{2325}(47, \cdot)\) n/a 2528 8
2325.2.dz \(\chi_{2325}(169, \cdot)\) n/a 1280 8
2325.2.eb \(\chi_{2325}(416, \cdot)\) n/a 2528 8
2325.2.ed \(\chi_{2325}(44, \cdot)\) n/a 2528 8
2325.2.eh \(\chi_{2325}(569, \cdot)\) n/a 2528 8
2325.2.ei \(\chi_{2325}(74, \cdot)\) n/a 1504 8
2325.2.ej \(\chi_{2325}(269, \cdot)\) n/a 2528 8
2325.2.eq \(\chi_{2325}(119, \cdot)\) n/a 2528 8
2325.2.es \(\chi_{2325}(161, \cdot)\) n/a 2528 8
2325.2.et \(\chi_{2325}(754, \cdot)\) n/a 1280 8
2325.2.ex \(\chi_{2325}(19, \cdot)\) n/a 1280 8
2325.2.ey \(\chi_{2325}(49, \cdot)\) n/a 768 8
2325.2.ez \(\chi_{2325}(214, \cdot)\) n/a 1280 8
2325.2.fb \(\chi_{2325}(446, \cdot)\) n/a 2528 8
2325.2.ff \(\chi_{2325}(176, \cdot)\) n/a 1576 8
2325.2.fg \(\chi_{2325}(146, \cdot)\) n/a 2528 8
2325.2.fh \(\chi_{2325}(11, \cdot)\) n/a 2528 8
2325.2.fk \(\chi_{2325}(304, \cdot)\) n/a 1280 8
2325.2.fm \(\chi_{2325}(104, \cdot)\) n/a 2528 8
2325.2.fo \(\chi_{2325}(13, \cdot)\) n/a 2560 16
2325.2.fp \(\chi_{2325}(227, \cdot)\) n/a 5056 16
2325.2.fu \(\chi_{2325}(608, \cdot)\) n/a 5056 16
2325.2.fv \(\chi_{2325}(22, \cdot)\) n/a 2560 16
2325.2.fw \(\chi_{2325}(43, \cdot)\) n/a 1536 16
2325.2.fx \(\chi_{2325}(37, \cdot)\) n/a 2560 16
2325.2.fy \(\chi_{2325}(107, \cdot)\) n/a 3008 16
2325.2.fz \(\chi_{2325}(98, \cdot)\) n/a 5056 16
2325.2.ga \(\chi_{2325}(152, \cdot)\) n/a 5056 16
2325.2.gb \(\chi_{2325}(73, \cdot)\) n/a 2560 16
2325.2.gk \(\chi_{2325}(292, \cdot)\) n/a 2560 16
2325.2.gl \(\chi_{2325}(38, \cdot)\) n/a 5056 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2325))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2325)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(775))\)\(^{\oplus 2}\)