Properties

Label 315.10.i
Level 315315
Weight 1010
Character orbit 315.i
Rep. character χ315(106,)\chi_{315}(106,\cdot)
Character field Q(ζ3)\Q(\zeta_{3})
Dimension 432432
Sturm bound 480480

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Defining parameters

Level: N N == 315=3257 315 = 3^{2} \cdot 5 \cdot 7
Weight: k k == 10 10
Character orbit: [χ][\chi] == 315.i (of order 33 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 9 9
Character field: Q(ζ3)\Q(\zeta_{3})
Sturm bound: 480480

Dimensions

The following table gives the dimensions of various subspaces of M10(315,[χ])M_{10}(315, [\chi]).

Total New Old
Modular forms 872 432 440
Cusp forms 856 432 424
Eisenstein series 16 0 16

Trace form

432q+64q2+292q355296q410460q661992q884916q9+116112q11853176q12+132500q1514155776q16+1453272q171922828q181575720q19++944973280q99+O(q100) 432 q + 64 q^{2} + 292 q^{3} - 55296 q^{4} - 10460 q^{6} - 61992 q^{8} - 84916 q^{9} + 116112 q^{11} - 853176 q^{12} + 132500 q^{15} - 14155776 q^{16} + 1453272 q^{17} - 1922828 q^{18} - 1575720 q^{19}+ \cdots + 944973280 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S10new(315,[χ])S_{10}^{\mathrm{new}}(315, [\chi]) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of S10old(315,[χ])S_{10}^{\mathrm{old}}(315, [\chi]) into lower level spaces

S10old(315,[χ]) S_{10}^{\mathrm{old}}(315, [\chi]) \simeq S10new(9,[χ])S_{10}^{\mathrm{new}}(9, [\chi])4^{\oplus 4}\oplusS10new(45,[χ])S_{10}^{\mathrm{new}}(45, [\chi])2^{\oplus 2}\oplusS10new(63,[χ])S_{10}^{\mathrm{new}}(63, [\chi])2^{\oplus 2}