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Properties

Label 210.6
Level 210
Weight 6
Dimension 1264
Nonzero newspaces 12
Sturm bound 13824
Trace bound 4

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Defining parameters

Level: \( N \) = \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(13824\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(210))\).

Total New Old
Modular forms 5952 1264 4688
Cusp forms 5568 1264 4304
Eisenstein series 384 0 384

Trace form

\( 1264 q + 8 q^{3} + 340 q^{5} + 128 q^{6} + 656 q^{7} - 816 q^{9} + O(q^{10}) \) \( 1264 q + 8 q^{3} + 340 q^{5} + 128 q^{6} + 656 q^{7} - 816 q^{9} - 752 q^{10} - 1936 q^{11} - 128 q^{12} + 2960 q^{13} + 1408 q^{14} - 1828 q^{15} + 6144 q^{16} - 216 q^{17} + 1568 q^{18} - 7456 q^{19} - 3328 q^{20} - 12836 q^{21} + 6592 q^{22} + 4392 q^{23} + 6144 q^{24} + 1416 q^{25} + 6432 q^{26} + 27296 q^{27} + 18304 q^{28} + 28080 q^{29} - 14832 q^{30} - 102800 q^{31} - 43792 q^{33} - 17472 q^{34} - 97280 q^{35} - 67456 q^{36} + 163440 q^{37} + 18336 q^{38} + 14520 q^{39} - 31488 q^{40} - 49984 q^{41} + 1808 q^{42} - 100608 q^{43} - 12032 q^{44} - 99608 q^{45} - 60160 q^{46} - 92136 q^{47} - 2048 q^{48} + 6896 q^{49} + 134272 q^{50} + 572704 q^{51} + 140288 q^{52} + 30504 q^{53} + 132480 q^{54} - 177660 q^{55} - 90112 q^{56} - 452584 q^{57} - 261088 q^{58} - 150928 q^{59} - 106240 q^{60} - 205264 q^{61} + 243840 q^{62} - 26168 q^{63} + 196608 q^{64} - 100308 q^{65} - 59584 q^{66} - 312688 q^{67} - 3456 q^{68} + 184176 q^{69} + 199584 q^{70} - 182544 q^{71} - 25088 q^{72} - 232376 q^{73} - 58144 q^{74} - 361952 q^{75} + 94720 q^{76} + 306984 q^{77} - 86112 q^{78} + 224032 q^{79} + 87040 q^{80} + 710032 q^{81} + 58816 q^{82} - 512112 q^{83} - 133824 q^{84} - 960320 q^{85} - 179360 q^{86} - 863008 q^{87} - 123392 q^{88} + 55120 q^{89} - 303664 q^{90} + 329984 q^{91} + 546816 q^{92} + 993512 q^{93} + 739584 q^{94} + 1003980 q^{95} - 57344 q^{96} + 681224 q^{97} - 142080 q^{98} + 1698672 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(210))\)

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
210.6.a \(\chi_{210}(1, \cdot)\) 210.6.a.a 1 1
210.6.a.b 1
210.6.a.c 1
210.6.a.d 1
210.6.a.e 1
210.6.a.f 1
210.6.a.g 1
210.6.a.h 1
210.6.a.i 1
210.6.a.j 1
210.6.a.k 2
210.6.a.l 2
210.6.a.m 2
210.6.a.n 2
210.6.a.o 2
210.6.b \(\chi_{210}(41, \cdot)\) 210.6.b.a 28 1
210.6.b.b 28
210.6.d \(\chi_{210}(209, \cdot)\) 210.6.d.a 40 1
210.6.d.b 40
210.6.g \(\chi_{210}(169, \cdot)\) 210.6.g.a 6 1
210.6.g.b 6
210.6.g.c 8
210.6.g.d 8
210.6.i \(\chi_{210}(121, \cdot)\) 210.6.i.a 2 2
210.6.i.b 4
210.6.i.c 6
210.6.i.d 6
210.6.i.e 6
210.6.i.f 8
210.6.i.g 8
210.6.i.h 8
210.6.i.i 8
210.6.j \(\chi_{210}(113, \cdot)\) n/a 120 2
210.6.m \(\chi_{210}(13, \cdot)\) 210.6.m.a 40 2
210.6.m.b 40
210.6.n \(\chi_{210}(79, \cdot)\) 210.6.n.a 36 2
210.6.n.b 44
210.6.r \(\chi_{210}(101, \cdot)\) n/a 104 2
210.6.t \(\chi_{210}(59, \cdot)\) n/a 160 2
210.6.u \(\chi_{210}(73, \cdot)\) n/a 160 4
210.6.x \(\chi_{210}(23, \cdot)\) n/a 320 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(210))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(210)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)