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Properties

Label 1110.6
Level 1110
Weight 6
Dimension 37564
Nonzero newspaces 30
Sturm bound 393984
Trace bound 8

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Defining parameters

Level: \( N \) = \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(393984\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1110))\).

Total New Old
Modular forms 165312 37564 127748
Cusp forms 163008 37564 125444
Eisenstein series 2304 0 2304

Trace form

\( 37564 q - 28 q^{3} + 128 q^{4} + 208 q^{5} - 304 q^{6} - 544 q^{7} + 648 q^{9} + O(q^{10}) \) \( 37564 q - 28 q^{3} + 128 q^{4} + 208 q^{5} - 304 q^{6} - 544 q^{7} + 648 q^{9} + 736 q^{10} - 160 q^{11} - 704 q^{12} - 6368 q^{13} + 2816 q^{14} - 5860 q^{15} + 6144 q^{16} + 6288 q^{17} + 4544 q^{18} - 4448 q^{19} - 3328 q^{20} - 6256 q^{21} + 6592 q^{22} + 12048 q^{23} + 2304 q^{24} + 37320 q^{25} + 104688 q^{26} - 18532 q^{27} - 32512 q^{28} - 152976 q^{29} - 93936 q^{30} - 403536 q^{31} + 42368 q^{33} + 258048 q^{34} + 323288 q^{35} + 52160 q^{36} + 478640 q^{37} + 155904 q^{38} + 115920 q^{39} - 13440 q^{40} - 382192 q^{41} - 296768 q^{42} - 710816 q^{43} - 44288 q^{44} - 80672 q^{45} - 587392 q^{46} - 55248 q^{47} + 44032 q^{48} + 1260408 q^{49} + 249592 q^{50} + 367144 q^{51} + 67072 q^{52} + 3936 q^{53} + 11664 q^{54} + 213792 q^{55} - 11264 q^{56} - 322816 q^{57} - 7168 q^{58} + 842240 q^{59} - 44608 q^{60} - 841340 q^{61} - 34752 q^{62} - 658120 q^{63} + 32768 q^{64} - 393534 q^{65} + 271040 q^{66} + 93296 q^{67} + 100608 q^{68} + 903744 q^{69} + 177408 q^{70} + 1197600 q^{71} - 72704 q^{72} + 579984 q^{73} - 309728 q^{74} - 74600 q^{75} - 39936 q^{76} + 479904 q^{77} + 112224 q^{78} + 178576 q^{79} + 53248 q^{80} - 950216 q^{81} + 571648 q^{82} - 1246512 q^{83} + 11520 q^{84} - 1196702 q^{85} + 256576 q^{86} - 1486528 q^{87} + 105472 q^{88} + 897316 q^{89} + 213920 q^{90} + 2952848 q^{91} + 192768 q^{92} - 1993000 q^{93} - 348672 q^{94} + 66000 q^{95} + 4096 q^{96} + 655936 q^{97} + 206976 q^{98} + 3913992 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1110))\)

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
1110.6.a \(\chi_{1110}(1, \cdot)\) 1110.6.a.a 1 1
1110.6.a.b 5
1110.6.a.c 6
1110.6.a.d 6
1110.6.a.e 6
1110.6.a.f 7
1110.6.a.g 7
1110.6.a.h 7
1110.6.a.i 7
1110.6.a.j 8
1110.6.a.k 8
1110.6.a.l 8
1110.6.a.m 8
1110.6.a.n 8
1110.6.a.o 9
1110.6.a.p 9
1110.6.a.q 10
1110.6.d \(\chi_{1110}(889, \cdot)\) n/a 180 1
1110.6.e \(\chi_{1110}(739, \cdot)\) n/a 188 1
1110.6.h \(\chi_{1110}(961, \cdot)\) n/a 124 1
1110.6.i \(\chi_{1110}(121, \cdot)\) n/a 248 2
1110.6.k \(\chi_{1110}(179, \cdot)\) n/a 760 2
1110.6.l \(\chi_{1110}(43, \cdot)\) n/a 380 2
1110.6.m \(\chi_{1110}(593, \cdot)\) n/a 720 2
1110.6.n \(\chi_{1110}(443, \cdot)\) n/a 760 2
1110.6.o \(\chi_{1110}(253, \cdot)\) n/a 380 2
1110.6.u \(\chi_{1110}(191, \cdot)\) n/a 512 2
1110.6.x \(\chi_{1110}(751, \cdot)\) n/a 248 2
1110.6.ba \(\chi_{1110}(529, \cdot)\) n/a 376 2
1110.6.bb \(\chi_{1110}(1009, \cdot)\) n/a 384 2
1110.6.bc \(\chi_{1110}(181, \cdot)\) n/a 768 6
1110.6.be \(\chi_{1110}(251, \cdot)\) n/a 1024 4
1110.6.bf \(\chi_{1110}(97, \cdot)\) n/a 760 4
1110.6.bg \(\chi_{1110}(233, \cdot)\) n/a 1520 4
1110.6.bh \(\chi_{1110}(47, \cdot)\) n/a 1520 4
1110.6.bi \(\chi_{1110}(193, \cdot)\) n/a 760 4
1110.6.bo \(\chi_{1110}(29, \cdot)\) n/a 1520 4
1110.6.bp \(\chi_{1110}(139, \cdot)\) n/a 1128 6
1110.6.bq \(\chi_{1110}(49, \cdot)\) n/a 1152 6
1110.6.br \(\chi_{1110}(151, \cdot)\) n/a 768 6
1110.6.by \(\chi_{1110}(59, \cdot)\) n/a 4560 12
1110.6.bz \(\chi_{1110}(131, \cdot)\) n/a 3024 12
1110.6.cc \(\chi_{1110}(163, \cdot)\) n/a 2280 12
1110.6.cd \(\chi_{1110}(53, \cdot)\) n/a 4560 12
1110.6.cg \(\chi_{1110}(77, \cdot)\) n/a 4560 12
1110.6.ch \(\chi_{1110}(13, \cdot)\) n/a 2280 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1110))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(1110)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(555))\)\(^{\oplus 2}\)