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Properties

Label 450.7
Level 450
Weight 7
Dimension 7880
Nonzero newspaces 12
Sturm bound 75600
Trace bound 4

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Defining parameters

Level: \( N \) = \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(75600\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(450))\).

Total New Old
Modular forms 32848 7880 24968
Cusp forms 31952 7880 24072
Eisenstein series 896 0 896

Trace form

\( 7880 q - 16 q^{2} - 42 q^{3} + 128 q^{4} - 180 q^{5} - 144 q^{6} + 664 q^{7} + 512 q^{8} + 4750 q^{9} + O(q^{10}) \) \( 7880 q - 16 q^{2} - 42 q^{3} + 128 q^{4} - 180 q^{5} - 144 q^{6} + 664 q^{7} + 512 q^{8} + 4750 q^{9} + 3096 q^{10} - 9782 q^{11} - 7808 q^{12} - 11540 q^{13} - 4752 q^{14} + 14784 q^{15} + 8192 q^{16} + 70620 q^{17} + 6752 q^{18} - 14372 q^{19} - 30464 q^{20} - 68436 q^{21} - 88464 q^{22} + 149864 q^{23} - 6144 q^{24} + 48942 q^{25} - 34048 q^{26} - 43008 q^{27} + 67072 q^{28} + 146692 q^{29} + 216928 q^{31} - 24576 q^{32} + 706126 q^{33} - 39384 q^{34} - 172856 q^{35} - 277184 q^{36} - 294932 q^{37} + 27040 q^{38} + 740764 q^{39} - 29952 q^{40} + 1258862 q^{41} + 964672 q^{42} + 9094 q^{43} - 471680 q^{45} + 486624 q^{46} - 2210860 q^{47} - 468992 q^{48} + 1801260 q^{49} - 219832 q^{50} + 446226 q^{51} - 115328 q^{52} + 2223296 q^{53} + 2564400 q^{54} - 1370040 q^{55} + 402944 q^{56} - 809194 q^{57} - 439344 q^{58} + 541178 q^{59} + 974848 q^{60} - 303932 q^{61} - 3925504 q^{62} - 3748728 q^{63} - 458752 q^{64} - 1758998 q^{65} + 960672 q^{66} + 3707326 q^{67} + 4577728 q^{68} + 8255272 q^{69} + 6874464 q^{70} - 4650400 q^{71} - 374784 q^{72} - 3076880 q^{73} - 2197152 q^{74} - 5883296 q^{75} - 638528 q^{76} - 15475432 q^{77} - 7119168 q^{78} - 4944308 q^{79} + 184320 q^{80} + 1687750 q^{81} - 2891952 q^{82} + 7155764 q^{83} + 3192576 q^{84} + 8758140 q^{85} - 785040 q^{86} + 17051900 q^{87} - 26112 q^{88} + 25795850 q^{89} + 7083776 q^{90} + 7317056 q^{91} - 5316352 q^{92} - 22650032 q^{93} - 207888 q^{94} - 9516712 q^{95} - 966656 q^{96} - 8905598 q^{97} - 15855248 q^{98} - 8167916 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(450))\)

We only show spaces with odd 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
450.7.b \(\chi_{450}(449, \cdot)\) 450.7.b.a 4 1
450.7.b.b 8
450.7.b.c 8
450.7.b.d 8
450.7.b.e 8
450.7.d \(\chi_{450}(251, \cdot)\) 450.7.d.a 2 1
450.7.d.b 4
450.7.d.c 4
450.7.d.d 4
450.7.d.e 4
450.7.d.f 4
450.7.d.g 4
450.7.d.h 6
450.7.d.i 6
450.7.g \(\chi_{450}(307, \cdot)\) 450.7.g.a 2 2
450.7.g.b 2
450.7.g.c 2
450.7.g.d 4
450.7.g.e 4
450.7.g.f 4
450.7.g.g 4
450.7.g.h 4
450.7.g.i 4
450.7.g.j 4
450.7.g.k 4
450.7.g.l 4
450.7.g.m 4
450.7.g.n 4
450.7.g.o 4
450.7.g.p 6
450.7.g.q 6
450.7.g.r 8
450.7.g.s 8
450.7.g.t 8
450.7.i \(\chi_{450}(101, \cdot)\) n/a 228 2
450.7.k \(\chi_{450}(149, \cdot)\) n/a 216 2
450.7.m \(\chi_{450}(89, \cdot)\) n/a 240 4
450.7.n \(\chi_{450}(71, \cdot)\) n/a 240 4
450.7.o \(\chi_{450}(7, \cdot)\) n/a 432 4
450.7.r \(\chi_{450}(37, \cdot)\) n/a 600 8
450.7.t \(\chi_{450}(11, \cdot)\) n/a 1440 8
450.7.u \(\chi_{450}(29, \cdot)\) n/a 1440 8
450.7.x \(\chi_{450}(13, \cdot)\) n/a 2880 16

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(450))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(450)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)