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Properties

Label 204.4
Level 204
Weight 4
Dimension 1470
Nonzero newspaces 10
Newform subspaces 14
Sturm bound 9216
Trace bound 1

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Defining parameters

Level: \( N \) = \( 204 = 2^{2} \cdot 3 \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 14 \)
Sturm bound: \(9216\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(204))\).

Total New Old
Modular forms 3616 1526 2090
Cusp forms 3296 1470 1826
Eisenstein series 320 56 264

Trace form

\( 1470 q - 6 q^{3} + 36 q^{5} + 40 q^{6} - 16 q^{7} - 10 q^{9} + O(q^{10}) \) \( 1470 q - 6 q^{3} + 36 q^{5} + 40 q^{6} - 16 q^{7} - 10 q^{9} - 176 q^{10} + 152 q^{11} - 248 q^{12} + 4 q^{13} - 228 q^{15} + 416 q^{16} - 274 q^{17} + 464 q^{18} + 40 q^{19} - 208 q^{21} - 496 q^{22} + 272 q^{23} - 1496 q^{24} - 1454 q^{25} - 1472 q^{26} - 54 q^{27} + 752 q^{28} + 988 q^{29} + 1816 q^{30} + 1760 q^{31} + 2480 q^{32} + 1768 q^{33} + 3888 q^{34} + 2272 q^{35} + 376 q^{36} + 2804 q^{37} + 1040 q^{38} - 1156 q^{39} - 1808 q^{40} - 1100 q^{41} - 2360 q^{42} - 3640 q^{43} - 4928 q^{44} - 1764 q^{45} - 2608 q^{46} - 864 q^{47} + 1168 q^{48} - 1738 q^{49} + 1546 q^{51} - 192 q^{52} - 4260 q^{53} + 3008 q^{54} - 1552 q^{55} + 5200 q^{56} - 720 q^{57} + 5280 q^{58} + 1208 q^{59} + 768 q^{60} + 5060 q^{61} - 4144 q^{62} - 432 q^{63} - 8112 q^{64} + 12816 q^{65} - 9104 q^{66} + 1480 q^{67} - 11792 q^{68} + 5584 q^{69} - 11840 q^{70} + 5616 q^{71} - 2976 q^{72} + 8468 q^{73} - 2400 q^{74} - 474 q^{75} - 3776 q^{76} - 4576 q^{77} + 3984 q^{78} - 6560 q^{79} + 9968 q^{80} - 4610 q^{81} + 13664 q^{82} - 7096 q^{83} + 16864 q^{84} - 12228 q^{85} + 2892 q^{87} + 5744 q^{88} - 1812 q^{89} + 5192 q^{90} - 3872 q^{91} - 9120 q^{93} + 2672 q^{94} - 1936 q^{95} - 11568 q^{96} + 524 q^{97} - 1280 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(204))\)

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
204.4.a \(\chi_{204}(1, \cdot)\) 204.4.a.a 1 1
204.4.a.b 2
204.4.a.c 2
204.4.a.d 3
204.4.b \(\chi_{204}(169, \cdot)\) 204.4.b.a 10 1
204.4.c \(\chi_{204}(35, \cdot)\) 204.4.c.a 96 1
204.4.h \(\chi_{204}(203, \cdot)\) 204.4.h.a 8 1
204.4.h.b 96
204.4.j \(\chi_{204}(13, \cdot)\) 204.4.j.a 20 2
204.4.l \(\chi_{204}(47, \cdot)\) 204.4.l.a 208 2
204.4.o \(\chi_{204}(25, \cdot)\) 204.4.o.a 32 4
204.4.p \(\chi_{204}(59, \cdot)\) 204.4.p.a 416 4
204.4.q \(\chi_{204}(5, \cdot)\) 204.4.q.a 144 8
204.4.r \(\chi_{204}(7, \cdot)\) 204.4.r.a 432 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(204))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(204)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)