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Properties

Label 200.14
Level 200
Weight 14
Dimension 8048
Nonzero newspaces 10
Sturm bound 33600
Trace bound 2

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Defining parameters

Level: \( N \) = \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(33600\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(200))\).

Total New Old
Modular forms 15768 8130 7638
Cusp forms 15432 8048 7384
Eisenstein series 336 82 254

Trace form

\( 8048 q - 14 q^{2} + 848 q^{3} - 8568 q^{4} - 8839 q^{5} + 58424 q^{6} + 532148 q^{7} + 1076860 q^{8} + 1995293 q^{9} + O(q^{10}) \) \( 8048 q - 14 q^{2} + 848 q^{3} - 8568 q^{4} - 8839 q^{5} + 58424 q^{6} + 532148 q^{7} + 1076860 q^{8} + 1995293 q^{9} - 16 q^{10} + 68520 q^{11} - 21291260 q^{12} - 42816938 q^{13} + 263050396 q^{14} - 78455944 q^{15} - 225546532 q^{16} - 86678806 q^{17} + 195348606 q^{18} - 922503968 q^{19} - 146915636 q^{20} + 1129229360 q^{21} + 2409807032 q^{22} - 3959333900 q^{23} - 7945257588 q^{24} + 1716239313 q^{25} + 11780231456 q^{26} - 7920407596 q^{27} - 17917956772 q^{28} + 29413896774 q^{29} + 15566733900 q^{30} + 4740406140 q^{31} - 48871111364 q^{32} - 12617304376 q^{33} + 103674487312 q^{34} + 31328910452 q^{35} - 124333818248 q^{36} - 44362929551 q^{37} + 59640198728 q^{38} - 245854364100 q^{39} + 84779822424 q^{40} - 8501317570 q^{41} - 452342889876 q^{42} + 51733917872 q^{43} + 105177502484 q^{44} + 255519176741 q^{45} + 768794295436 q^{46} - 110260675644 q^{47} - 2063791716068 q^{48} + 304027180596 q^{49} + 1003620036164 q^{50} - 851245688796 q^{51} - 1934208952140 q^{52} + 227241189529 q^{53} + 8661696564 q^{54} - 313187052808 q^{55} + 2364066647356 q^{56} - 1104527465784 q^{57} - 1413671273124 q^{58} - 1808687637728 q^{59} - 1872668605020 q^{60} + 396328161570 q^{61} + 4508305584524 q^{62} + 5313779007468 q^{63} - 2373629748756 q^{64} - 4579791418079 q^{65} + 1608038492404 q^{66} - 4970122460752 q^{67} - 8770448577556 q^{68} + 7819926333776 q^{69} + 8495769205540 q^{70} + 10544657071780 q^{71} - 1111417870728 q^{72} - 11403425116622 q^{73} - 9027305951540 q^{74} - 1949054522264 q^{75} - 111429703120 q^{76} - 2337437667424 q^{77} + 9062685733004 q^{78} + 19245474284156 q^{79} + 7841344352324 q^{80} - 21080620840719 q^{81} - 40792123333536 q^{82} - 18643691697876 q^{83} + 35151643170316 q^{84} + 5741596783393 q^{85} - 26612299638800 q^{86} - 7512957373972 q^{87} - 4234652447636 q^{88} - 2079140768763 q^{89} + 136213294931684 q^{90} - 16482098890108 q^{91} - 12169197058924 q^{92} - 26518637557640 q^{93} - 141248794984516 q^{94} - 47850643048608 q^{95} - 23705185751036 q^{96} + 30859437349398 q^{97} + 140066245131194 q^{98} + 218289756731808 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(200))\)

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
200.14.a \(\chi_{200}(1, \cdot)\) 200.14.a.a 1 1
200.14.a.b 2
200.14.a.c 3
200.14.a.d 3
200.14.a.e 3
200.14.a.f 4
200.14.a.g 6
200.14.a.h 6
200.14.a.i 7
200.14.a.j 7
200.14.a.k 10
200.14.a.l 10
200.14.c \(\chi_{200}(49, \cdot)\) 200.14.c.a 2 1
200.14.c.b 4
200.14.c.c 6
200.14.c.d 6
200.14.c.e 6
200.14.c.f 8
200.14.c.g 12
200.14.c.h 14
200.14.d \(\chi_{200}(101, \cdot)\) n/a 244 1
200.14.f \(\chi_{200}(149, \cdot)\) n/a 232 1
200.14.j \(\chi_{200}(7, \cdot)\) None 0 2
200.14.k \(\chi_{200}(43, \cdot)\) n/a 464 2
200.14.m \(\chi_{200}(41, \cdot)\) n/a 388 4
200.14.o \(\chi_{200}(29, \cdot)\) n/a 1552 4
200.14.q \(\chi_{200}(9, \cdot)\) n/a 392 4
200.14.t \(\chi_{200}(21, \cdot)\) n/a 1552 4
200.14.v \(\chi_{200}(3, \cdot)\) n/a 3104 8
200.14.w \(\chi_{200}(23, \cdot)\) None 0 8

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(200)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)