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Properties

Label 630.6
Level 630
Weight 6
Dimension 12022
Nonzero newspaces 30
Sturm bound 124416
Trace bound 15

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(124416\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(630))\).

Total New Old
Modular forms 52608 12022 40586
Cusp forms 51072 12022 39050
Eisenstein series 1536 0 1536

Trace form

\( 12022 q - 24 q^{2} + 36 q^{3} - 96 q^{4} - 320 q^{5} - 336 q^{6} - 508 q^{7} + 384 q^{8} + 2812 q^{9} + O(q^{10}) \) \( 12022 q - 24 q^{2} + 36 q^{3} - 96 q^{4} - 320 q^{5} - 336 q^{6} - 508 q^{7} + 384 q^{8} + 2812 q^{9} - 1856 q^{10} - 5044 q^{11} - 1280 q^{12} + 7544 q^{13} + 928 q^{14} + 7416 q^{15} - 7680 q^{16} + 444 q^{17} + 7136 q^{18} + 4628 q^{19} - 4672 q^{20} + 4788 q^{21} + 4720 q^{22} - 35016 q^{23} - 5376 q^{24} + 14274 q^{25} + 1056 q^{26} + 32376 q^{27} - 12416 q^{28} + 24756 q^{29} + 7824 q^{30} + 118792 q^{31} - 6144 q^{32} - 188372 q^{33} - 34944 q^{34} - 32546 q^{35} + 18880 q^{36} - 134364 q^{37} + 37056 q^{38} + 74152 q^{39} + 27648 q^{40} + 360320 q^{41} - 7744 q^{42} + 114228 q^{43} + 11776 q^{44} - 280984 q^{45} + 167360 q^{46} + 8136 q^{47} + 7168 q^{48} - 98710 q^{49} + 12952 q^{50} + 31500 q^{51} - 187648 q^{52} + 593004 q^{53} + 332112 q^{54} + 149808 q^{55} + 11264 q^{56} + 238796 q^{57} + 271280 q^{58} + 258680 q^{59} - 15488 q^{60} + 394040 q^{61} - 378912 q^{62} - 1300376 q^{63} + 122880 q^{64} - 745164 q^{65} - 362112 q^{66} + 104684 q^{67} - 57984 q^{68} + 433400 q^{69} - 286872 q^{70} - 34896 q^{71} - 238848 q^{72} - 183500 q^{73} + 979280 q^{74} + 939648 q^{75} + 454528 q^{76} + 198516 q^{77} + 46304 q^{78} + 1249912 q^{79} + 83968 q^{80} + 981908 q^{81} + 503344 q^{82} + 471276 q^{83} - 199488 q^{84} - 181016 q^{85} - 2689040 q^{86} - 2478200 q^{87} - 286976 q^{88} - 1018532 q^{89} + 39616 q^{90} + 363668 q^{91} - 20352 q^{92} - 449560 q^{93} + 29280 q^{94} + 881424 q^{95} + 90112 q^{96} + 300392 q^{97} + 1099992 q^{98} + 3765592 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(630))\)

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
630.6.a \(\chi_{630}(1, \cdot)\) 630.6.a.a 1 1
630.6.a.b 1
630.6.a.c 1
630.6.a.d 1
630.6.a.e 1
630.6.a.f 1
630.6.a.g 1
630.6.a.h 1
630.6.a.i 1
630.6.a.j 1
630.6.a.k 1
630.6.a.l 1
630.6.a.m 1
630.6.a.n 1
630.6.a.o 1
630.6.a.p 1
630.6.a.q 2
630.6.a.r 2
630.6.a.s 2
630.6.a.t 2
630.6.a.u 2
630.6.a.v 2
630.6.a.w 2
630.6.a.x 2
630.6.a.y 2
630.6.a.z 2
630.6.a.ba 2
630.6.a.bb 3
630.6.a.bc 3
630.6.a.bd 3
630.6.a.be 3
630.6.b \(\chi_{630}(251, \cdot)\) 630.6.b.a 24 1
630.6.b.b 24
630.6.d \(\chi_{630}(629, \cdot)\) 630.6.d.a 40 1
630.6.d.b 40
630.6.g \(\chi_{630}(379, \cdot)\) 630.6.g.a 2 1
630.6.g.b 2
630.6.g.c 2
630.6.g.d 6
630.6.g.e 6
630.6.g.f 8
630.6.g.g 8
630.6.g.h 10
630.6.g.i 16
630.6.g.j 16
630.6.i \(\chi_{630}(121, \cdot)\) n/a 320 2
630.6.j \(\chi_{630}(211, \cdot)\) n/a 240 2
630.6.k \(\chi_{630}(361, \cdot)\) n/a 136 2
630.6.l \(\chi_{630}(331, \cdot)\) n/a 320 2
630.6.m \(\chi_{630}(197, \cdot)\) n/a 120 2
630.6.p \(\chi_{630}(307, \cdot)\) n/a 200 2
630.6.r \(\chi_{630}(59, \cdot)\) n/a 480 2
630.6.t \(\chi_{630}(311, \cdot)\) n/a 320 2
630.6.u \(\chi_{630}(109, \cdot)\) n/a 200 2
630.6.z \(\chi_{630}(169, \cdot)\) n/a 360 2
630.6.ba \(\chi_{630}(499, \cdot)\) n/a 480 2
630.6.be \(\chi_{630}(341, \cdot)\) n/a 112 2
630.6.bf \(\chi_{630}(209, \cdot)\) n/a 480 2
630.6.bi \(\chi_{630}(479, \cdot)\) n/a 480 2
630.6.bk \(\chi_{630}(101, \cdot)\) n/a 320 2
630.6.bl \(\chi_{630}(41, \cdot)\) n/a 320 2
630.6.bo \(\chi_{630}(89, \cdot)\) n/a 160 2
630.6.bq \(\chi_{630}(79, \cdot)\) n/a 480 2
630.6.bt \(\chi_{630}(317, \cdot)\) n/a 960 4
630.6.bv \(\chi_{630}(73, \cdot)\) n/a 400 4
630.6.bw \(\chi_{630}(103, \cdot)\) n/a 960 4
630.6.bz \(\chi_{630}(13, \cdot)\) n/a 960 4
630.6.ca \(\chi_{630}(113, \cdot)\) n/a 720 4
630.6.cd \(\chi_{630}(23, \cdot)\) n/a 960 4
630.6.ce \(\chi_{630}(53, \cdot)\) n/a 320 4
630.6.cg \(\chi_{630}(157, \cdot)\) n/a 960 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(630))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(630)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 1}\)