Properties

Label 1075.4
Level 1075
Weight 4
Dimension 126764
Nonzero newspaces 24
Sturm bound 369600
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(369600\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1075))\).

Total New Old
Modular forms 139776 128444 11332
Cusp forms 137424 126764 10660
Eisenstein series 2352 1680 672

Trace form

\( 126764 q - 269 q^{2} - 245 q^{3} - 221 q^{4} - 326 q^{5} - 437 q^{6} - 229 q^{7} - 253 q^{8} - 345 q^{9} + O(q^{10}) \) \( 126764 q - 269 q^{2} - 245 q^{3} - 221 q^{4} - 326 q^{5} - 437 q^{6} - 229 q^{7} - 253 q^{8} - 345 q^{9} - 276 q^{10} - 277 q^{11} - 189 q^{12} - 405 q^{13} - 349 q^{14} - 336 q^{15} - 149 q^{16} + 491 q^{17} + 1015 q^{18} + 387 q^{19} - 676 q^{20} - 837 q^{21} - 2205 q^{22} - 1445 q^{23} - 3113 q^{24} - 1706 q^{25} - 1077 q^{26} - 1733 q^{27} - 1501 q^{28} - 613 q^{29} + 244 q^{30} - 747 q^{31} + 155 q^{32} - 93 q^{33} + 741 q^{34} + 1344 q^{35} + 1611 q^{36} + 2385 q^{37} + 4975 q^{38} + 5793 q^{39} + 3784 q^{40} + 1443 q^{41} + 4462 q^{42} + 4751 q^{43} + 1198 q^{44} - 4726 q^{45} - 1077 q^{46} - 5287 q^{47} - 10809 q^{48} - 5871 q^{49} - 9336 q^{50} - 7497 q^{51} - 14425 q^{52} - 6431 q^{53} - 11863 q^{54} - 2156 q^{55} - 6101 q^{56} + 491 q^{57} + 3767 q^{58} + 8347 q^{59} + 22604 q^{60} + 5163 q^{61} + 22015 q^{62} + 15635 q^{63} + 13119 q^{64} + 3574 q^{65} + 1787 q^{66} - 1189 q^{67} - 7101 q^{68} - 14891 q^{69} - 8716 q^{70} - 8967 q^{71} - 39123 q^{72} - 12507 q^{73} - 26198 q^{74} - 12056 q^{75} - 8836 q^{76} - 8727 q^{77} - 2980 q^{78} + 1439 q^{79} - 11996 q^{80} + 15471 q^{81} + 28405 q^{82} + 21071 q^{83} + 57737 q^{84} + 18954 q^{85} + 18781 q^{86} + 33824 q^{87} + 38051 q^{88} + 20529 q^{89} + 15984 q^{90} + 6903 q^{91} + 16241 q^{92} - 4565 q^{93} - 11925 q^{94} - 13956 q^{95} - 16822 q^{96} - 30671 q^{97} - 32778 q^{98} - 41196 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1075))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1075.4.a \(\chi_{1075}(1, \cdot)\) 1075.4.a.a 4 1
1075.4.a.b 6
1075.4.a.c 6
1075.4.a.d 8
1075.4.a.e 13
1075.4.a.f 15
1075.4.a.g 19
1075.4.a.h 19
1075.4.a.i 23
1075.4.a.j 23
1075.4.a.k 32
1075.4.a.l 32
1075.4.b \(\chi_{1075}(474, \cdot)\) n/a 188 1
1075.4.e \(\chi_{1075}(251, \cdot)\) n/a 412 2
1075.4.g \(\chi_{1075}(257, \cdot)\) n/a 392 2
1075.4.h \(\chi_{1075}(216, \cdot)\) n/a 1256 4
1075.4.j \(\chi_{1075}(49, \cdot)\) n/a 392 2
1075.4.l \(\chi_{1075}(176, \cdot)\) n/a 1236 6
1075.4.o \(\chi_{1075}(44, \cdot)\) n/a 1264 4
1075.4.p \(\chi_{1075}(7, \cdot)\) n/a 784 4
1075.4.t \(\chi_{1075}(274, \cdot)\) n/a 1176 6
1075.4.u \(\chi_{1075}(6, \cdot)\) n/a 2624 8
1075.4.v \(\chi_{1075}(42, \cdot)\) n/a 2624 8
1075.4.x \(\chi_{1075}(101, \cdot)\) n/a 2472 12
1075.4.y \(\chi_{1075}(32, \cdot)\) n/a 2352 12
1075.4.bb \(\chi_{1075}(79, \cdot)\) n/a 2624 8
1075.4.bd \(\chi_{1075}(11, \cdot)\) n/a 7872 24
1075.4.bf \(\chi_{1075}(24, \cdot)\) n/a 2352 12
1075.4.bi \(\chi_{1075}(37, \cdot)\) n/a 5248 16
1075.4.bj \(\chi_{1075}(4, \cdot)\) n/a 7872 24
1075.4.bn \(\chi_{1075}(18, \cdot)\) n/a 4704 24
1075.4.bo \(\chi_{1075}(31, \cdot)\) n/a 15744 48
1075.4.bq \(\chi_{1075}(2, \cdot)\) n/a 15744 48
1075.4.bs \(\chi_{1075}(9, \cdot)\) n/a 15744 48
1075.4.bu \(\chi_{1075}(3, \cdot)\) n/a 31488 96

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1075))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1075)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 2}\)