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

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

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

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