Properties

Label 315.10.bz
Level 315315
Weight 1010
Character orbit 315.bz
Rep. character χ315(73,)\chi_{315}(73,\cdot)
Character field Q(ζ12)\Q(\zeta_{12})
Dimension 712712
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.bz (of order 1212 and degree 44)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 35 35
Character field: Q(ζ12)\Q(\zeta_{12})
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 1760 728 1032
Cusp forms 1696 712 984
Eisenstein series 64 16 48

Trace form

712q+2q21698q513572q7+628q8153798q1026096q11+22007172q16+1578678q172128008q225311142q231461706q25+2294604q2620603030q28+11494866q98+O(q100) 712 q + 2 q^{2} - 1698 q^{5} - 13572 q^{7} + 628 q^{8} - 153798 q^{10} - 26096 q^{11} + 22007172 q^{16} + 1578678 q^{17} - 2128008 q^{22} - 5311142 q^{23} - 1461706 q^{25} + 2294604 q^{26} - 20603030 q^{28}+ \cdots - 11494866 q^{98}+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(35,[χ])S_{10}^{\mathrm{new}}(35, [\chi])3^{\oplus 3}\oplusS10new(105,[χ])S_{10}^{\mathrm{new}}(105, [\chi])2^{\oplus 2}