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Properties

Label 203.5
Level 203
Weight 5
Dimension 6290
Nonzero newspaces 12
Sturm bound 16800
Trace bound 2

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Defining parameters

Level: \( N \) = \( 203 = 7 \cdot 29 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(16800\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(203))\).

Total New Old
Modular forms 6888 6558 330
Cusp forms 6552 6290 262
Eisenstein series 336 268 68

Trace form

\( 6290 q - 50 q^{2} - 68 q^{3} + 14 q^{4} + 4 q^{5} - 56 q^{6} - 168 q^{7} - 686 q^{8} - 170 q^{9} + O(q^{10}) \) \( 6290 q - 50 q^{2} - 68 q^{3} + 14 q^{4} + 4 q^{5} - 56 q^{6} - 168 q^{7} - 686 q^{8} - 170 q^{9} + 352 q^{10} + 472 q^{11} + 1120 q^{12} - 56 q^{13} - 1288 q^{14} - 1076 q^{15} - 330 q^{16} + 436 q^{17} - 650 q^{18} - 1340 q^{19} - 8120 q^{20} + 658 q^{21} + 5488 q^{22} + 3772 q^{23} + 20008 q^{24} + 6726 q^{25} + 4648 q^{26} + 4396 q^{27} + 1442 q^{28} - 2390 q^{29} - 18784 q^{30} - 16196 q^{31} - 26138 q^{32} - 21416 q^{33} - 13496 q^{34} + 770 q^{35} - 5198 q^{36} + 4836 q^{37} + 25720 q^{38} + 29288 q^{39} + 35704 q^{40} - 56 q^{41} - 12166 q^{42} - 4416 q^{43} - 40544 q^{44} - 49304 q^{45} - 48016 q^{46} - 332 q^{47} + 30184 q^{48} + 12320 q^{49} + 53446 q^{50} + 53764 q^{51} + 94808 q^{52} + 65488 q^{53} + 96820 q^{54} + 47432 q^{55} + 16086 q^{56} - 22272 q^{57} - 39026 q^{58} - 17932 q^{59} - 109984 q^{60} - 46980 q^{61} - 97076 q^{62} - 67816 q^{63} - 123274 q^{64} - 78176 q^{65} - 97760 q^{66} - 45392 q^{67} - 73220 q^{68} + 8008 q^{69} - 16534 q^{70} - 47396 q^{71} + 55354 q^{72} + 95972 q^{73} + 69640 q^{74} + 63876 q^{75} + 116424 q^{76} + 83888 q^{77} + 182868 q^{78} + 66184 q^{79} + 297880 q^{80} + 121650 q^{81} + 74312 q^{82} + 52696 q^{83} + 52724 q^{84} + 59236 q^{85} - 25272 q^{86} - 30252 q^{87} - 122644 q^{88} - 139016 q^{89} - 181468 q^{90} - 101290 q^{91} - 280064 q^{92} - 122356 q^{93} - 166696 q^{94} - 232916 q^{95} - 630420 q^{96} - 274344 q^{97} - 109774 q^{98} - 248156 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(203))\)

We only show spaces with odd 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
203.5.c \(\chi_{203}(202, \cdot)\) 203.5.c.a 1 1
203.5.c.b 1
203.5.c.c 2
203.5.c.d 2
203.5.c.e 72
203.5.d \(\chi_{203}(146, \cdot)\) 203.5.d.a 76 1
203.5.f \(\chi_{203}(99, \cdot)\) n/a 120 2
203.5.h \(\chi_{203}(59, \cdot)\) n/a 148 2
203.5.i \(\chi_{203}(115, \cdot)\) n/a 156 2
203.5.m \(\chi_{203}(46, \cdot)\) n/a 312 4
203.5.n \(\chi_{203}(20, \cdot)\) n/a 468 6
203.5.o \(\chi_{203}(6, \cdot)\) n/a 468 6
203.5.s \(\chi_{203}(8, \cdot)\) n/a 720 12
203.5.u \(\chi_{203}(5, \cdot)\) n/a 936 12
203.5.v \(\chi_{203}(24, \cdot)\) n/a 936 12
203.5.w \(\chi_{203}(2, \cdot)\) n/a 1872 24

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(203))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(203)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(203))\)\(^{\oplus 1}\)