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Properties

Label 1450.4
Level 1450
Weight 4
Dimension 57927
Nonzero newspaces 24
Sturm bound 504000
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(504000\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1450))\).

Total New Old
Modular forms 190568 57927 132641
Cusp forms 187432 57927 129505
Eisenstein series 3136 0 3136

Trace form

\( 57927 q + 8 q^{2} - 32 q^{3} - 16 q^{4} - 10 q^{5} - 32 q^{6} - 16 q^{7} + 32 q^{8} + 332 q^{9} + O(q^{10}) \) \( 57927 q + 8 q^{2} - 32 q^{3} - 16 q^{4} - 10 q^{5} - 32 q^{6} - 16 q^{7} + 32 q^{8} + 332 q^{9} + 100 q^{10} - 176 q^{11} - 128 q^{12} - 232 q^{13} - 448 q^{14} - 160 q^{15} + 192 q^{16} - 1016 q^{17} - 604 q^{18} - 400 q^{19} + 160 q^{20} + 3072 q^{21} + 1928 q^{22} + 2344 q^{23} + 352 q^{24} + 2630 q^{25} - 162 q^{26} - 344 q^{27} + 416 q^{28} - 1948 q^{29} - 720 q^{30} - 3088 q^{31} - 192 q^{32} - 4896 q^{33} - 1678 q^{34} - 2440 q^{35} + 640 q^{36} + 26 q^{37} + 936 q^{38} + 1376 q^{39} - 240 q^{40} - 736 q^{41} + 256 q^{42} + 688 q^{43} + 1088 q^{44} + 4550 q^{45} + 128 q^{46} + 4108 q^{47} - 512 q^{48} + 1278 q^{49} - 700 q^{50} + 1664 q^{51} - 928 q^{52} + 1887 q^{53} + 960 q^{54} + 2200 q^{55} + 1536 q^{56} - 1112 q^{57} - 360 q^{58} - 9620 q^{59} - 5440 q^{60} - 6536 q^{61} - 8624 q^{62} - 25856 q^{63} - 256 q^{64} - 6170 q^{65} - 1424 q^{66} + 632 q^{67} + 4896 q^{68} + 13224 q^{69} + 9600 q^{70} + 19060 q^{71} + 1184 q^{72} + 24749 q^{73} + 16632 q^{74} + 24080 q^{75} + 3584 q^{76} + 22128 q^{77} + 14544 q^{78} + 12080 q^{79} - 160 q^{80} - 5492 q^{81} - 4320 q^{82} - 14360 q^{83} - 9792 q^{84} - 13210 q^{85} - 12952 q^{86} - 21080 q^{87} + 384 q^{88} - 31350 q^{89} - 17340 q^{90} - 21344 q^{91} - 11872 q^{92} - 15952 q^{93} - 6928 q^{94} + 4120 q^{95} - 512 q^{96} + 11077 q^{97} + 2536 q^{98} + 27096 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1450))\)

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
1450.4.a \(\chi_{1450}(1, \cdot)\) 1450.4.a.a 1 1
1450.4.a.b 1
1450.4.a.c 1
1450.4.a.d 1
1450.4.a.e 1
1450.4.a.f 1
1450.4.a.g 2
1450.4.a.h 3
1450.4.a.i 3
1450.4.a.j 3
1450.4.a.k 3
1450.4.a.l 5
1450.4.a.m 5
1450.4.a.n 5
1450.4.a.o 6
1450.4.a.p 6
1450.4.a.q 7
1450.4.a.r 7
1450.4.a.s 7
1450.4.a.t 7
1450.4.a.u 8
1450.4.a.v 8
1450.4.a.w 9
1450.4.a.x 9
1450.4.a.y 12
1450.4.a.z 12
1450.4.b \(\chi_{1450}(349, \cdot)\) n/a 126 1
1450.4.c \(\chi_{1450}(1101, \cdot)\) n/a 142 1
1450.4.d \(\chi_{1450}(1449, \cdot)\) n/a 136 1
1450.4.e \(\chi_{1450}(307, \cdot)\) n/a 270 2
1450.4.j \(\chi_{1450}(157, \cdot)\) n/a 270 2
1450.4.k \(\chi_{1450}(291, \cdot)\) n/a 840 4
1450.4.l \(\chi_{1450}(401, \cdot)\) n/a 858 6
1450.4.m \(\chi_{1450}(289, \cdot)\) n/a 896 4
1450.4.n \(\chi_{1450}(59, \cdot)\) n/a 840 4
1450.4.o \(\chi_{1450}(231, \cdot)\) n/a 904 4
1450.4.p \(\chi_{1450}(149, \cdot)\) n/a 816 6
1450.4.q \(\chi_{1450}(51, \cdot)\) n/a 852 6
1450.4.r \(\chi_{1450}(49, \cdot)\) n/a 804 6
1450.4.s \(\chi_{1450}(133, \cdot)\) n/a 1800 8
1450.4.x \(\chi_{1450}(17, \cdot)\) n/a 1800 8
1450.4.y \(\chi_{1450}(43, \cdot)\) n/a 1620 12
1450.4.bd \(\chi_{1450}(143, \cdot)\) n/a 1620 12
1450.4.be \(\chi_{1450}(81, \cdot)\) n/a 5376 24
1450.4.bf \(\chi_{1450}(71, \cdot)\) n/a 5424 24
1450.4.bg \(\chi_{1450}(139, \cdot)\) n/a 5424 24
1450.4.bh \(\chi_{1450}(9, \cdot)\) n/a 5376 24
1450.4.bi \(\chi_{1450}(73, \cdot)\) n/a 10800 48
1450.4.bn \(\chi_{1450}(3, \cdot)\) n/a 10800 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1450))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1450)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(725))\)\(^{\oplus 2}\)