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Properties

Label 1445.4
Level 1445
Weight 4
Dimension 226201
Nonzero newspaces 20
Sturm bound 665856
Trace bound 8

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Defining parameters

Level: \( N \) = \( 1445 = 5 \cdot 17^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(665856\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1445))\).

Total New Old
Modular forms 251296 228411 22885
Cusp forms 248096 226201 21895
Eisenstein series 3200 2210 990

Trace form

\( 226201 q - 244 q^{2} - 238 q^{3} - 232 q^{4} - 365 q^{5} - 728 q^{6} - 234 q^{7} - 240 q^{8} - 263 q^{9} + O(q^{10}) \) \( 226201 q - 244 q^{2} - 238 q^{3} - 232 q^{4} - 365 q^{5} - 728 q^{6} - 234 q^{7} - 240 q^{8} - 263 q^{9} - 548 q^{10} - 1136 q^{11} - 608 q^{12} - 150 q^{13} + 376 q^{14} + 302 q^{15} + 976 q^{16} + 1420 q^{18} + 180 q^{19} - 176 q^{20} - 1092 q^{21} - 1264 q^{22} - 1150 q^{23} - 7728 q^{24} - 2791 q^{25} - 4696 q^{26} - 1204 q^{27} + 384 q^{28} + 750 q^{29} + 2368 q^{30} + 2628 q^{31} + 4720 q^{32} + 4016 q^{33} + 3968 q^{34} + 1258 q^{35} + 5752 q^{36} + 2714 q^{37} - 1952 q^{38} - 5180 q^{39} - 5352 q^{40} - 6378 q^{41} - 12000 q^{42} - 5654 q^{43} - 7792 q^{44} - 2925 q^{45} - 4440 q^{46} + 5326 q^{47} + 12848 q^{48} + 5597 q^{49} + 1124 q^{50} + 2432 q^{51} + 11520 q^{52} - 1470 q^{53} - 10592 q^{54} - 4296 q^{55} - 4720 q^{56} - 8392 q^{57} - 5960 q^{58} - 3196 q^{59} - 3272 q^{60} - 278 q^{61} - 7264 q^{62} + 7494 q^{63} - 5040 q^{64} + 2030 q^{65} + 19728 q^{66} + 8430 q^{67} + 16048 q^{68} + 34324 q^{69} + 34560 q^{70} + 13004 q^{71} + 34544 q^{72} + 15442 q^{73} + 7240 q^{74} + 2954 q^{75} - 4112 q^{76} - 8048 q^{77} - 28576 q^{78} - 14872 q^{79} - 42728 q^{80} - 39883 q^{81} - 44424 q^{82} - 37686 q^{83} - 97968 q^{84} - 20820 q^{85} - 58136 q^{86} - 36244 q^{87} - 48624 q^{88} - 17094 q^{89} - 32292 q^{90} - 11316 q^{91} - 4896 q^{92} + 5432 q^{93} + 20632 q^{94} + 13572 q^{95} + 48336 q^{96} + 19730 q^{97} + 63516 q^{98} + 28912 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1445))\)

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
1445.4.a \(\chi_{1445}(1, \cdot)\) 1445.4.a.a 1 1
1445.4.a.b 1
1445.4.a.c 1
1445.4.a.d 1
1445.4.a.e 1
1445.4.a.f 1
1445.4.a.g 1
1445.4.a.h 1
1445.4.a.i 2
1445.4.a.j 3
1445.4.a.k 3
1445.4.a.l 5
1445.4.a.m 7
1445.4.a.n 7
1445.4.a.o 8
1445.4.a.p 8
1445.4.a.q 8
1445.4.a.r 8
1445.4.a.s 18
1445.4.a.t 18
1445.4.a.u 21
1445.4.a.v 21
1445.4.a.w 27
1445.4.a.x 27
1445.4.a.y 36
1445.4.a.z 36
1445.4.b \(\chi_{1445}(579, \cdot)\) n/a 392 1
1445.4.c \(\chi_{1445}(1444, \cdot)\) n/a 392 1
1445.4.d \(\chi_{1445}(866, \cdot)\) n/a 270 1
1445.4.e \(\chi_{1445}(251, \cdot)\) n/a 540 2
1445.4.j \(\chi_{1445}(829, \cdot)\) n/a 784 2
1445.4.l \(\chi_{1445}(1001, \cdot)\) n/a 1080 4
1445.4.m \(\chi_{1445}(134, \cdot)\) n/a 1560 4
1445.4.o \(\chi_{1445}(158, \cdot)\) n/a 3128 8
1445.4.r \(\chi_{1445}(447, \cdot)\) n/a 3128 8
1445.4.s \(\chi_{1445}(86, \cdot)\) n/a 4896 16
1445.4.t \(\chi_{1445}(16, \cdot)\) n/a 4896 16
1445.4.u \(\chi_{1445}(84, \cdot)\) n/a 7296 16
1445.4.v \(\chi_{1445}(69, \cdot)\) n/a 7296 16
1445.4.w \(\chi_{1445}(4, \cdot)\) n/a 14592 32
1445.4.bb \(\chi_{1445}(21, \cdot)\) n/a 9792 32
1445.4.bd \(\chi_{1445}(9, \cdot)\) n/a 29312 64
1445.4.be \(\chi_{1445}(26, \cdot)\) n/a 19584 64
1445.4.bg \(\chi_{1445}(12, \cdot)\) n/a 58496 128
1445.4.bj \(\chi_{1445}(3, \cdot)\) n/a 58496 128

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1445))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1445)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 2}\)