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Properties

Label 450.6
Level 450
Weight 6
Dimension 6568
Nonzero newspaces 12
Sturm bound 64800
Trace bound 3

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Defining parameters

Level: \( N \) = \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(64800\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(450))\).

Total New Old
Modular forms 27448 6568 20880
Cusp forms 26552 6568 19984
Eisenstein series 896 0 896

Trace form

\( 6568 q + 9 q^{3} - 64 q^{4} - 85 q^{5} - 84 q^{6} + 446 q^{7} + 192 q^{8} + 1075 q^{9} + O(q^{10}) \) \( 6568 q + 9 q^{3} - 64 q^{4} - 85 q^{5} - 84 q^{6} + 446 q^{7} + 192 q^{8} + 1075 q^{9} - 1804 q^{10} - 4933 q^{11} - 128 q^{12} + 7192 q^{13} + 7880 q^{14} + 4344 q^{15} - 3072 q^{16} - 2264 q^{17} - 6520 q^{18} - 35886 q^{19} - 6784 q^{20} - 11070 q^{21} + 9948 q^{22} + 8702 q^{23} + 576 q^{24} + 15127 q^{25} + 19192 q^{26} + 38352 q^{27} + 3840 q^{28} + 31700 q^{29} - 412 q^{31} - 5120 q^{32} - 131909 q^{33} - 8512 q^{34} + 17684 q^{35} + 41200 q^{36} - 167229 q^{37} + 85284 q^{38} + 88480 q^{39} - 192 q^{40} + 72729 q^{41} - 126368 q^{42} + 8897 q^{43} - 12704 q^{44} - 151280 q^{45} + 146000 q^{46} + 37934 q^{47} - 4352 q^{48} + 40377 q^{49} + 62628 q^{50} + 175941 q^{51} - 70016 q^{52} + 243723 q^{53} + 198660 q^{54} - 156020 q^{55} + 11392 q^{56} - 107197 q^{57} + 64688 q^{58} - 566087 q^{59} - 215552 q^{60} + 99078 q^{61} + 347664 q^{62} + 624516 q^{63} + 45056 q^{64} + 1217047 q^{65} + 181344 q^{66} + 96251 q^{67} + 65808 q^{68} - 198764 q^{69} - 412416 q^{70} - 499488 q^{71} - 59712 q^{72} - 460032 q^{73} - 808840 q^{74} - 1271336 q^{75} - 64368 q^{76} - 280518 q^{77} - 70680 q^{78} - 193436 q^{79} - 21760 q^{80} + 799567 q^{81} + 789760 q^{82} + 2123680 q^{83} + 584352 q^{84} + 1657135 q^{85} + 683428 q^{86} + 492602 q^{87} + 8128 q^{88} - 1067197 q^{89} - 638464 q^{90} - 1547576 q^{91} - 1596768 q^{92} - 3031004 q^{93} - 855288 q^{94} - 582772 q^{95} - 69632 q^{96} - 306763 q^{97} + 665100 q^{98} + 2569762 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(450))\)

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
450.6.a \(\chi_{450}(1, \cdot)\) 450.6.a.a 1 1
450.6.a.b 1
450.6.a.c 1
450.6.a.d 1
450.6.a.e 1
450.6.a.f 1
450.6.a.g 1
450.6.a.h 1
450.6.a.i 1
450.6.a.j 1
450.6.a.k 1
450.6.a.l 1
450.6.a.m 1
450.6.a.n 1
450.6.a.o 1
450.6.a.p 1
450.6.a.q 1
450.6.a.r 1
450.6.a.s 1
450.6.a.t 1
450.6.a.u 1
450.6.a.v 1
450.6.a.w 1
450.6.a.x 1
450.6.a.y 2
450.6.a.z 2
450.6.a.ba 2
450.6.a.bb 2
450.6.a.bc 2
450.6.a.bd 2
450.6.a.be 2
450.6.a.bf 2
450.6.c \(\chi_{450}(199, \cdot)\) 450.6.c.a 2 1
450.6.c.b 2
450.6.c.c 2
450.6.c.d 2
450.6.c.e 2
450.6.c.f 2
450.6.c.g 2
450.6.c.h 2
450.6.c.i 2
450.6.c.j 2
450.6.c.k 2
450.6.c.l 2
450.6.c.m 2
450.6.c.n 2
450.6.c.o 2
450.6.c.p 4
450.6.c.q 4
450.6.e \(\chi_{450}(151, \cdot)\) n/a 190 2
450.6.f \(\chi_{450}(107, \cdot)\) 450.6.f.a 4 2
450.6.f.b 4
450.6.f.c 4
450.6.f.d 4
450.6.f.e 12
450.6.f.f 16
450.6.f.g 16
450.6.h \(\chi_{450}(91, \cdot)\) n/a 252 4
450.6.j \(\chi_{450}(49, \cdot)\) n/a 180 2
450.6.l \(\chi_{450}(19, \cdot)\) n/a 248 4
450.6.p \(\chi_{450}(257, \cdot)\) n/a 360 4
450.6.q \(\chi_{450}(31, \cdot)\) n/a 1200 8
450.6.s \(\chi_{450}(17, \cdot)\) n/a 400 8
450.6.v \(\chi_{450}(79, \cdot)\) n/a 1200 8
450.6.w \(\chi_{450}(23, \cdot)\) n/a 2400 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(450))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(450)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)