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Properties

Label 575.6
Level 575
Weight 6
Dimension 60169
Nonzero newspaces 12
Sturm bound 158400
Trace bound 2

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Defining parameters

Level: \( N \) = \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(158400\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(575))\).

Total New Old
Modular forms 66616 61029 5587
Cusp forms 65384 60169 5215
Eisenstein series 1232 860 372

Trace form

\( 60169 q - 115 q^{2} - 139 q^{3} - 331 q^{4} - 286 q^{5} + 829 q^{6} + 645 q^{7} - 603 q^{8} - 2255 q^{9} + O(q^{10}) \) \( 60169 q - 115 q^{2} - 139 q^{3} - 331 q^{4} - 286 q^{5} + 829 q^{6} + 645 q^{7} - 603 q^{8} - 2255 q^{9} - 936 q^{10} + 1229 q^{11} + 325 q^{12} + 1021 q^{13} + 4581 q^{14} + 2284 q^{15} + 4381 q^{16} + 956 q^{17} - 5643 q^{18} - 14422 q^{19} - 20676 q^{20} - 27078 q^{21} + 6914 q^{22} + 4897 q^{23} + 71850 q^{24} + 37854 q^{25} + 30381 q^{26} + 34400 q^{27} - 16571 q^{28} - 86332 q^{29} - 107836 q^{30} - 3650 q^{31} - 82523 q^{32} - 53776 q^{33} - 5149 q^{34} + 80584 q^{35} + 167514 q^{36} + 133931 q^{37} + 241572 q^{38} + 23353 q^{39} - 179656 q^{40} - 122489 q^{41} - 486277 q^{42} - 184375 q^{43} - 250536 q^{44} + 35394 q^{45} - 169753 q^{46} + 11178 q^{47} + 455697 q^{48} + 382029 q^{49} + 504724 q^{50} + 228113 q^{51} + 496355 q^{52} + 214113 q^{53} + 87617 q^{54} - 182436 q^{55} - 174586 q^{56} - 472374 q^{57} - 572024 q^{58} - 298913 q^{59} - 195156 q^{60} + 187009 q^{61} - 84391 q^{62} - 165874 q^{63} - 384831 q^{64} - 272506 q^{65} - 429044 q^{66} - 87313 q^{67} - 764326 q^{68} - 65920 q^{69} + 234948 q^{70} + 376154 q^{71} + 1063216 q^{72} + 243123 q^{73} + 189372 q^{74} + 621404 q^{75} + 833994 q^{76} + 898292 q^{77} + 1536751 q^{78} + 1014701 q^{79} - 4156 q^{80} + 1127737 q^{81} + 1242583 q^{82} - 10732 q^{83} - 1685725 q^{84} - 1362506 q^{85} - 2793741 q^{86} - 2709771 q^{87} - 3517347 q^{88} - 1597667 q^{89} - 1508996 q^{90} - 865310 q^{91} - 282760 q^{92} - 216306 q^{93} + 602148 q^{94} + 2452088 q^{95} + 6628516 q^{96} + 3861652 q^{97} + 2941149 q^{98} + 389110 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(575))\)

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
575.6.a \(\chi_{575}(1, \cdot)\) 575.6.a.a 2 1
575.6.a.b 3
575.6.a.c 6
575.6.a.d 7
575.6.a.e 7
575.6.a.f 10
575.6.a.g 12
575.6.a.h 15
575.6.a.i 15
575.6.a.j 21
575.6.a.k 21
575.6.a.l 27
575.6.a.m 27
575.6.b \(\chi_{575}(24, \cdot)\) n/a 166 1
575.6.e \(\chi_{575}(68, \cdot)\) n/a 356 2
575.6.g \(\chi_{575}(116, \cdot)\) n/a 1104 4
575.6.i \(\chi_{575}(139, \cdot)\) n/a 1096 4
575.6.k \(\chi_{575}(26, \cdot)\) n/a 1870 10
575.6.m \(\chi_{575}(22, \cdot)\) n/a 2384 8
575.6.p \(\chi_{575}(49, \cdot)\) n/a 1780 10
575.6.r \(\chi_{575}(7, \cdot)\) n/a 3560 20
575.6.s \(\chi_{575}(6, \cdot)\) n/a 11920 40
575.6.u \(\chi_{575}(4, \cdot)\) n/a 11920 40
575.6.w \(\chi_{575}(17, \cdot)\) n/a 23840 80

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(575))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(575)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)