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Properties

Label 2541.2
Level 2541
Weight 2
Dimension 162824
Nonzero newspaces 32
Sturm bound 929280
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(929280\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2541))\).

Total New Old
Modular forms 236160 165636 70524
Cusp forms 228481 162824 65657
Eisenstein series 7679 2812 4867

Trace form

\( 162824 q - 6 q^{2} - 184 q^{3} - 372 q^{4} - 6 q^{5} - 160 q^{6} - 436 q^{7} + 68 q^{8} - 138 q^{9} + O(q^{10}) \) \( 162824 q - 6 q^{2} - 184 q^{3} - 372 q^{4} - 6 q^{5} - 160 q^{6} - 436 q^{7} + 68 q^{8} - 138 q^{9} - 252 q^{10} + 20 q^{11} - 264 q^{12} - 334 q^{13} + 60 q^{14} - 382 q^{15} - 152 q^{16} + 96 q^{17} - 126 q^{18} - 266 q^{19} + 152 q^{20} - 179 q^{21} - 880 q^{22} + 56 q^{23} - 92 q^{24} - 226 q^{25} + 158 q^{26} - 238 q^{27} - 340 q^{28} + 56 q^{29} - 172 q^{30} - 306 q^{31} + 20 q^{32} - 220 q^{33} - 568 q^{34} + 74 q^{35} - 446 q^{36} - 236 q^{37} + 134 q^{38} - 94 q^{39} - 16 q^{40} + 180 q^{41} - 167 q^{42} - 668 q^{43} + 220 q^{44} - 166 q^{45} + 88 q^{46} + 238 q^{47} + 80 q^{48} - 232 q^{49} + 344 q^{50} + 16 q^{51} + 56 q^{52} + 220 q^{53} - 126 q^{54} - 240 q^{55} + 222 q^{56} - 466 q^{57} - 96 q^{58} + 84 q^{59} - 476 q^{60} - 342 q^{61} - 60 q^{62} - 421 q^{63} - 1100 q^{64} - 198 q^{65} - 450 q^{66} - 790 q^{67} - 440 q^{68} - 464 q^{69} - 906 q^{70} - 324 q^{71} - 932 q^{72} - 464 q^{73} - 246 q^{74} - 526 q^{75} - 1060 q^{76} - 90 q^{77} - 1166 q^{78} - 282 q^{79} - 552 q^{80} - 630 q^{81} - 508 q^{82} + 76 q^{83} - 825 q^{84} - 956 q^{85} - 298 q^{86} - 256 q^{87} - 440 q^{88} - 40 q^{89} - 424 q^{90} - 598 q^{91} + 32 q^{92} - 96 q^{93} - 132 q^{94} + 354 q^{95} - 460 q^{96} + 28 q^{97} + 440 q^{98} - 440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2541))\)

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
2541.2.a \(\chi_{2541}(1, \cdot)\) 2541.2.a.a 1 1
2541.2.a.b 1
2541.2.a.c 1
2541.2.a.d 1
2541.2.a.e 1
2541.2.a.f 1
2541.2.a.g 1
2541.2.a.h 1
2541.2.a.i 1
2541.2.a.j 1
2541.2.a.k 1
2541.2.a.l 1
2541.2.a.m 2
2541.2.a.n 2
2541.2.a.o 2
2541.2.a.p 2
2541.2.a.q 2
2541.2.a.r 2
2541.2.a.s 2
2541.2.a.t 2
2541.2.a.u 2
2541.2.a.v 2
2541.2.a.w 2
2541.2.a.x 2
2541.2.a.y 2
2541.2.a.z 2
2541.2.a.ba 2
2541.2.a.bb 2
2541.2.a.bc 2
2541.2.a.bd 2
2541.2.a.be 2
2541.2.a.bf 2
2541.2.a.bg 3
2541.2.a.bh 3
2541.2.a.bi 3
2541.2.a.bj 3
2541.2.a.bk 4
2541.2.a.bl 4
2541.2.a.bm 4
2541.2.a.bn 4
2541.2.a.bo 4
2541.2.a.bp 4
2541.2.a.bq 10
2541.2.a.br 10
2541.2.c \(\chi_{2541}(1693, \cdot)\) n/a 144 1
2541.2.e \(\chi_{2541}(1574, \cdot)\) n/a 272 1
2541.2.g \(\chi_{2541}(1814, \cdot)\) n/a 216 1
2541.2.i \(\chi_{2541}(1453, \cdot)\) n/a 290 2
2541.2.j \(\chi_{2541}(148, \cdot)\) n/a 432 4
2541.2.l \(\chi_{2541}(725, \cdot)\) n/a 544 2
2541.2.n \(\chi_{2541}(122, \cdot)\) n/a 546 2
2541.2.p \(\chi_{2541}(241, \cdot)\) n/a 288 2
2541.2.s \(\chi_{2541}(239, \cdot)\) n/a 864 4
2541.2.u \(\chi_{2541}(251, \cdot)\) n/a 1088 4
2541.2.w \(\chi_{2541}(118, \cdot)\) n/a 576 4
2541.2.y \(\chi_{2541}(232, \cdot)\) n/a 1320 10
2541.2.z \(\chi_{2541}(130, \cdot)\) n/a 1152 8
2541.2.bb \(\chi_{2541}(197, \cdot)\) n/a 2640 10
2541.2.bd \(\chi_{2541}(188, \cdot)\) n/a 3480 10
2541.2.bf \(\chi_{2541}(76, \cdot)\) n/a 1760 10
2541.2.bi \(\chi_{2541}(40, \cdot)\) n/a 1152 8
2541.2.bk \(\chi_{2541}(269, \cdot)\) n/a 2176 8
2541.2.bm \(\chi_{2541}(233, \cdot)\) n/a 2176 8
2541.2.bo \(\chi_{2541}(67, \cdot)\) n/a 3520 20
2541.2.bp \(\chi_{2541}(64, \cdot)\) n/a 5280 40
2541.2.br \(\chi_{2541}(10, \cdot)\) n/a 3520 20
2541.2.bt \(\chi_{2541}(89, \cdot)\) n/a 6960 20
2541.2.bv \(\chi_{2541}(32, \cdot)\) n/a 6960 20
2541.2.by \(\chi_{2541}(13, \cdot)\) n/a 7040 40
2541.2.ca \(\chi_{2541}(20, \cdot)\) n/a 13920 40
2541.2.cc \(\chi_{2541}(8, \cdot)\) n/a 10560 40
2541.2.ce \(\chi_{2541}(4, \cdot)\) n/a 14080 80
2541.2.cg \(\chi_{2541}(2, \cdot)\) n/a 27840 80
2541.2.ci \(\chi_{2541}(5, \cdot)\) n/a 27840 80
2541.2.ck \(\chi_{2541}(19, \cdot)\) n/a 14080 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2541))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2541)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 2}\)