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Properties

Label 1805.4
Level 1805
Weight 4
Dimension 354007
Nonzero newspaces 18
Sturm bound 1039680
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(1039680\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1805))\).

Total New Old
Modular forms 391896 356817 35079
Cusp forms 387864 354007 33857
Eisenstein series 4032 2810 1222

Trace form

\( 354007 q - 310 q^{2} - 304 q^{3} - 298 q^{4} - 464 q^{5} - 926 q^{6} - 300 q^{7} - 306 q^{8} - 329 q^{9} + O(q^{10}) \) \( 354007 q - 310 q^{2} - 304 q^{3} - 298 q^{4} - 464 q^{5} - 926 q^{6} - 300 q^{7} - 306 q^{8} - 329 q^{9} - 439 q^{10} - 886 q^{11} - 1442 q^{12} - 920 q^{13} - 474 q^{14} - 253 q^{15} + 746 q^{16} + 296 q^{17} + 1694 q^{18} + 432 q^{19} + 221 q^{20} + 102 q^{21} + 214 q^{22} - 456 q^{23} - 2034 q^{24} - 1298 q^{25} - 3502 q^{26} - 5626 q^{27} - 9438 q^{28} - 2876 q^{29} - 2813 q^{30} - 1386 q^{31} + 1210 q^{32} + 3430 q^{33} + 4090 q^{34} + 1743 q^{35} + 11210 q^{36} + 2588 q^{37} + 4338 q^{38} + 6890 q^{39} + 3303 q^{40} + 904 q^{41} + 5766 q^{42} - 368 q^{43} - 11750 q^{44} - 6500 q^{45} - 14682 q^{46} - 8308 q^{47} - 22862 q^{48} - 7453 q^{49} - 4969 q^{50} - 1406 q^{51} + 8894 q^{52} + 6032 q^{53} + 9922 q^{54} + 3269 q^{55} + 23238 q^{56} + 4716 q^{57} + 7382 q^{58} + 9194 q^{59} + 2539 q^{60} - 12452 q^{61} - 13518 q^{62} - 13980 q^{63} - 17234 q^{64} - 5489 q^{65} - 15286 q^{66} - 3852 q^{67} - 14462 q^{68} - 1758 q^{69} + 309 q^{70} - 9218 q^{71} + 16146 q^{72} + 18580 q^{73} + 19366 q^{74} + 3173 q^{75} + 12528 q^{76} + 33510 q^{77} + 50182 q^{78} + 31974 q^{79} + 44213 q^{80} + 26755 q^{81} + 26354 q^{82} + 6816 q^{83} + 7998 q^{84} - 3613 q^{85} - 14674 q^{86} - 27766 q^{87} - 42354 q^{88} - 30480 q^{89} - 62569 q^{90} - 44634 q^{91} - 61734 q^{92} - 54738 q^{93} - 63734 q^{94} - 16344 q^{95} - 109846 q^{96} - 32320 q^{97} - 72986 q^{98} - 46798 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1805))\)

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
1805.4.a \(\chi_{1805}(1, \cdot)\) 1805.4.a.a 1 1
1805.4.a.b 1
1805.4.a.c 1
1805.4.a.d 1
1805.4.a.e 1
1805.4.a.f 1
1805.4.a.g 1
1805.4.a.h 1
1805.4.a.i 1
1805.4.a.j 3
1805.4.a.k 5
1805.4.a.l 6
1805.4.a.m 6
1805.4.a.n 9
1805.4.a.o 9
1805.4.a.p 10
1805.4.a.q 10
1805.4.a.r 10
1805.4.a.s 16
1805.4.a.t 16
1805.4.a.u 20
1805.4.a.v 20
1805.4.a.w 30
1805.4.a.x 30
1805.4.a.y 30
1805.4.a.z 30
1805.4.a.ba 32
1805.4.a.bb 40
1805.4.b \(\chi_{1805}(1084, \cdot)\) n/a 494 1
1805.4.e \(\chi_{1805}(1151, \cdot)\) n/a 680 2
1805.4.g \(\chi_{1805}(1082, \cdot)\) n/a 988 2
1805.4.i \(\chi_{1805}(429, \cdot)\) n/a 988 2
1805.4.k \(\chi_{1805}(606, \cdot)\) n/a 2040 6
1805.4.l \(\chi_{1805}(293, \cdot)\) n/a 1976 4
1805.4.p \(\chi_{1805}(54, \cdot)\) n/a 2964 6
1805.4.q \(\chi_{1805}(96, \cdot)\) n/a 6840 18
1805.4.s \(\chi_{1805}(127, \cdot)\) n/a 5928 12
1805.4.v \(\chi_{1805}(39, \cdot)\) n/a 10224 18
1805.4.w \(\chi_{1805}(11, \cdot)\) n/a 13680 36
1805.4.x \(\chi_{1805}(18, \cdot)\) n/a 20448 36
1805.4.ba \(\chi_{1805}(49, \cdot)\) n/a 20448 36
1805.4.bc \(\chi_{1805}(6, \cdot)\) n/a 41040 108
1805.4.be \(\chi_{1805}(8, \cdot)\) n/a 40896 72
1805.4.bf \(\chi_{1805}(4, \cdot)\) n/a 61344 108
1805.4.bi \(\chi_{1805}(2, \cdot)\) n/a 122688 216

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1805))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1805)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)