↑

Properties

Label 352.2.u
Level $352$
Weight $2$
Character orbit 352.u
Rep. character $\chi_{352}(63,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $48$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 352 = 2^{5} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 352.u (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(352, [\chi])\).

Total New Old
Modular forms 224 48 176
Cusp forms 160 48 112
Eisenstein series 64 0 64

Trace form

\( 48 q + 4 q^{9} + O(q^{10}) \) \( 48 q + 4 q^{9} + 4 q^{25} + 36 q^{33} + 40 q^{41} - 96 q^{45} - 4 q^{49} - 8 q^{53} + 20 q^{57} - 8 q^{69} - 40 q^{73} - 72 q^{77} - 72 q^{81} - 80 q^{85} - 40 q^{89} + 8 q^{93} + 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(352, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
352.2.u.a 352.u 44.g $48$ $2.811$ None 352.2.u.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(352, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)