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Properties

Label 1617.2
Level 1617
Weight 2
Dimension 65706
Nonzero newspaces 32
Sturm bound 376320
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(376320\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1617))\).

Total New Old
Modular forms 96480 67454 29026
Cusp forms 91681 65706 25975
Eisenstein series 4799 1748 3051

Trace form

\( 65706 q - 6 q^{2} - 123 q^{3} - 232 q^{4} + 12 q^{5} - 90 q^{6} - 272 q^{7} + 62 q^{8} - 89 q^{9} + O(q^{10}) \) \( 65706 q - 6 q^{2} - 123 q^{3} - 232 q^{4} + 12 q^{5} - 90 q^{6} - 272 q^{7} + 62 q^{8} - 89 q^{9} - 136 q^{10} + 34 q^{11} - 222 q^{12} - 188 q^{13} + 48 q^{14} - 189 q^{15} - 108 q^{16} + 42 q^{17} - 104 q^{18} - 180 q^{19} + 110 q^{20} - 130 q^{21} - 400 q^{22} + 68 q^{23} - 46 q^{24} - 104 q^{25} + 134 q^{26} - 114 q^{27} - 144 q^{28} + 104 q^{29} - 48 q^{30} - 118 q^{31} + 158 q^{32} - 120 q^{33} - 364 q^{34} + 84 q^{35} - 214 q^{36} - 214 q^{37} - 22 q^{38} - 158 q^{39} - 464 q^{40} - 96 q^{41} - 282 q^{42} - 420 q^{43} - 58 q^{44} - 295 q^{45} - 456 q^{46} + 22 q^{47} - 362 q^{48} - 516 q^{49} - 52 q^{50} - 214 q^{51} - 540 q^{52} - 14 q^{53} - 104 q^{54} - 326 q^{55} - 300 q^{56} - 150 q^{57} - 316 q^{58} + 78 q^{59} - 592 q^{60} - 368 q^{61} - 12 q^{62} - 198 q^{63} - 780 q^{64} - 108 q^{65} - 583 q^{66} - 598 q^{67} - 344 q^{68} - 355 q^{69} - 420 q^{70} - 324 q^{71} - 796 q^{72} - 468 q^{73} - 210 q^{74} - 546 q^{75} - 1076 q^{76} - 108 q^{77} - 1010 q^{78} - 304 q^{79} - 894 q^{80} - 785 q^{81} - 692 q^{82} - 398 q^{83} - 868 q^{84} - 816 q^{85} - 928 q^{86} - 648 q^{87} - 1086 q^{88} - 436 q^{89} - 1314 q^{90} - 584 q^{91} - 562 q^{92} - 749 q^{93} - 736 q^{94} - 426 q^{95} - 1020 q^{96} - 306 q^{97} - 876 q^{98} - 551 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1617))\)

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
1617.2.a \(\chi_{1617}(1, \cdot)\) 1617.2.a.a 1 1
1617.2.a.b 1
1617.2.a.c 1
1617.2.a.d 1
1617.2.a.e 1
1617.2.a.f 1
1617.2.a.g 1
1617.2.a.h 1
1617.2.a.i 1
1617.2.a.j 1
1617.2.a.k 2
1617.2.a.l 2
1617.2.a.m 2
1617.2.a.n 2
1617.2.a.o 2
1617.2.a.p 2
1617.2.a.q 3
1617.2.a.r 3
1617.2.a.s 3
1617.2.a.t 3
1617.2.a.u 4
1617.2.a.v 4
1617.2.a.w 4
1617.2.a.x 4
1617.2.a.y 4
1617.2.a.z 4
1617.2.a.ba 5
1617.2.a.bb 5
1617.2.c \(\chi_{1617}(538, \cdot)\) 1617.2.c.a 32 1
1617.2.c.b 48
1617.2.e \(\chi_{1617}(881, \cdot)\) n/a 132 1
1617.2.g \(\chi_{1617}(197, \cdot)\) n/a 154 1
1617.2.i \(\chi_{1617}(67, \cdot)\) n/a 132 2
1617.2.j \(\chi_{1617}(148, \cdot)\) n/a 328 4
1617.2.l \(\chi_{1617}(263, \cdot)\) n/a 304 2
1617.2.n \(\chi_{1617}(815, \cdot)\) n/a 268 2
1617.2.p \(\chi_{1617}(472, \cdot)\) n/a 160 2
1617.2.r \(\chi_{1617}(232, \cdot)\) n/a 552 6
1617.2.t \(\chi_{1617}(50, \cdot)\) n/a 616 4
1617.2.v \(\chi_{1617}(146, \cdot)\) n/a 608 4
1617.2.x \(\chi_{1617}(244, \cdot)\) n/a 320 4
1617.2.ba \(\chi_{1617}(428, \cdot)\) n/a 1320 6
1617.2.bc \(\chi_{1617}(188, \cdot)\) n/a 1128 6
1617.2.be \(\chi_{1617}(76, \cdot)\) n/a 672 6
1617.2.bg \(\chi_{1617}(214, \cdot)\) n/a 640 8
1617.2.bh \(\chi_{1617}(100, \cdot)\) n/a 1128 12
1617.2.bj \(\chi_{1617}(19, \cdot)\) n/a 640 8
1617.2.bl \(\chi_{1617}(80, \cdot)\) n/a 1216 8
1617.2.bn \(\chi_{1617}(116, \cdot)\) n/a 1216 8
1617.2.bp \(\chi_{1617}(64, \cdot)\) n/a 2688 24
1617.2.br \(\chi_{1617}(10, \cdot)\) n/a 1344 12
1617.2.bt \(\chi_{1617}(89, \cdot)\) n/a 2232 12
1617.2.bv \(\chi_{1617}(32, \cdot)\) n/a 2640 12
1617.2.by \(\chi_{1617}(13, \cdot)\) n/a 2688 24
1617.2.ca \(\chi_{1617}(20, \cdot)\) n/a 5280 24
1617.2.cc \(\chi_{1617}(8, \cdot)\) n/a 5280 24
1617.2.ce \(\chi_{1617}(4, \cdot)\) n/a 5376 48
1617.2.cg \(\chi_{1617}(2, \cdot)\) n/a 10560 48
1617.2.ci \(\chi_{1617}(5, \cdot)\) n/a 10560 48
1617.2.ck \(\chi_{1617}(40, \cdot)\) n/a 5376 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1617))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1617)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 2}\)