↑

Properties

Label 315.10.b
Level $315$
Weight $10$
Character orbit 315.b
Rep. character $\chi_{315}(251,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $2$
Sturm bound $480$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 315.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(5\)

Dimensions

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

Total New Old
Modular forms 440 96 344
Cusp forms 424 96 328
Eisenstein series 16 0 16

Trace form

\( 96 q - 24576 q^{4} + 3648 q^{7} + 6517896 q^{16} - 5721336 q^{22} + 37500000 q^{25} - 7370184 q^{28} + 15500688 q^{37} + 32147664 q^{43} - 30167640 q^{46} - 78735000 q^{49} + 587639880 q^{58} - 3279579648 q^{64}+ \cdots - 2325030120 q^{91}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
315.10.b.a 315.b 21.c $48$ $162.236$ None 315.10.b.a \(0\) \(0\) \(-30000\) \(1824\) $\mathrm{SU}(2)[C_{2}]$
315.10.b.b 315.b 21.c $48$ $162.236$ None 315.10.b.a \(0\) \(0\) \(30000\) \(1824\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)