Properties

Label 805.2
Level 805
Weight 2
Dimension 21555
Nonzero newspaces 24
Newform subspaces 60
Sturm bound 101376
Trace bound 5

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Defining parameters

Level: \( N \) = \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 60 \)
Sturm bound: \(101376\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(805))\).

Total New Old
Modular forms 26400 22811 3589
Cusp forms 24289 21555 2734
Eisenstein series 2111 1256 855

Trace form

\( 21555 q - 67 q^{2} - 68 q^{3} - 71 q^{4} - 117 q^{5} - 228 q^{6} - 99 q^{7} - 187 q^{8} - 77 q^{9} + O(q^{10}) \) \( 21555 q - 67 q^{2} - 68 q^{3} - 71 q^{4} - 117 q^{5} - 228 q^{6} - 99 q^{7} - 187 q^{8} - 77 q^{9} - 135 q^{10} - 228 q^{11} - 92 q^{12} - 78 q^{13} - 125 q^{14} - 340 q^{15} - 335 q^{16} - 126 q^{17} - 279 q^{18} - 128 q^{19} - 259 q^{20} - 400 q^{21} - 340 q^{22} - 165 q^{23} - 380 q^{24} - 177 q^{25} - 298 q^{26} - 164 q^{27} - 169 q^{28} - 198 q^{29} - 160 q^{30} - 244 q^{31} - 71 q^{32} - 36 q^{33} - 86 q^{34} - 160 q^{35} - 683 q^{36} - 206 q^{37} - 248 q^{38} - 176 q^{39} - 275 q^{40} - 298 q^{41} - 318 q^{42} - 344 q^{43} - 448 q^{44} - 307 q^{45} - 571 q^{46} - 352 q^{47} - 484 q^{48} - 315 q^{49} - 473 q^{50} - 464 q^{51} - 506 q^{52} - 206 q^{53} - 480 q^{54} - 300 q^{55} - 623 q^{56} - 464 q^{57} - 358 q^{58} - 292 q^{59} - 384 q^{60} - 310 q^{61} - 208 q^{62} - 173 q^{63} - 363 q^{64} - 244 q^{65} - 556 q^{66} - 28 q^{67} - 450 q^{68} - 192 q^{69} - 241 q^{70} - 760 q^{71} - 511 q^{72} - 34 q^{73} - 310 q^{74} - 354 q^{75} - 640 q^{76} - 296 q^{77} - 756 q^{78} - 304 q^{79} - 493 q^{80} - 897 q^{81} - 390 q^{82} - 360 q^{83} - 554 q^{84} - 612 q^{85} - 732 q^{86} - 592 q^{87} - 84 q^{88} - 298 q^{89} - 585 q^{90} - 566 q^{91} - 455 q^{92} - 640 q^{93} - 500 q^{94} - 206 q^{95} - 968 q^{96} - 150 q^{97} - 23 q^{98} - 444 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(805))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
805.2.a \(\chi_{805}(1, \cdot)\) 805.2.a.a 1 1
805.2.a.b 1
805.2.a.c 1
805.2.a.d 1
805.2.a.e 2
805.2.a.f 3
805.2.a.g 4
805.2.a.h 4
805.2.a.i 4
805.2.a.j 4
805.2.a.k 5
805.2.a.l 5
805.2.a.m 8
805.2.c \(\chi_{805}(484, \cdot)\) 805.2.c.a 2 1
805.2.c.b 24
805.2.c.c 42
805.2.d \(\chi_{805}(804, \cdot)\) 805.2.d.a 4 1
805.2.d.b 8
805.2.d.c 8
805.2.d.d 12
805.2.d.e 12
805.2.d.f 48
805.2.f \(\chi_{805}(321, \cdot)\) 805.2.f.a 32 1
805.2.f.b 32
805.2.i \(\chi_{805}(116, \cdot)\) 805.2.i.a 2 2
805.2.i.b 4
805.2.i.c 24
805.2.i.d 26
805.2.i.e 30
805.2.i.f 34
805.2.k \(\chi_{805}(622, \cdot)\) 805.2.k.a 176 2
805.2.l \(\chi_{805}(22, \cdot)\) 805.2.l.a 144 2
805.2.p \(\chi_{805}(206, \cdot)\) 805.2.p.a 64 2
805.2.p.b 64
805.2.r \(\chi_{805}(229, \cdot)\) 805.2.r.a 8 2
805.2.r.b 176
805.2.s \(\chi_{805}(254, \cdot)\) 805.2.s.a 4 2
805.2.s.b 4
805.2.s.c 4
805.2.s.d 164
805.2.u \(\chi_{805}(36, \cdot)\) 805.2.u.a 110 10
805.2.u.b 110
805.2.u.c 130
805.2.u.d 130
805.2.v \(\chi_{805}(47, \cdot)\) 805.2.v.a 352 4
805.2.y \(\chi_{805}(137, \cdot)\) 805.2.y.a 368 4
805.2.bb \(\chi_{805}(76, \cdot)\) 805.2.bb.a 320 10
805.2.bb.b 320
805.2.bd \(\chi_{805}(34, \cdot)\) 805.2.bd.a 920 10
805.2.be \(\chi_{805}(29, \cdot)\) 805.2.be.a 720 10
805.2.bg \(\chi_{805}(16, \cdot)\) 805.2.bg.a 600 20
805.2.bg.b 680
805.2.bi \(\chi_{805}(43, \cdot)\) 805.2.bi.a 1440 20
805.2.bj \(\chi_{805}(13, \cdot)\) 805.2.bj.a 1840 20
805.2.bm \(\chi_{805}(4, \cdot)\) 805.2.bm.a 1840 20
805.2.bn \(\chi_{805}(19, \cdot)\) 805.2.bn.a 1840 20
805.2.bp \(\chi_{805}(61, \cdot)\) 805.2.bp.a 640 20
805.2.bp.b 640
805.2.bs \(\chi_{805}(37, \cdot)\) 805.2.bs.a 3680 40
805.2.bv \(\chi_{805}(3, \cdot)\) 805.2.bv.a 3680 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(805))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(805)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)