↑

Properties

Label 238.2.p
Level $238$
Weight $2$
Character orbit 238.p
Rep. character $\chi_{238}(27,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $96$
Newform subspaces $2$
Sturm bound $72$
Trace bound $15$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 238 = 2 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 238.p (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(238, [\chi])\).

Total New Old
Modular forms 320 96 224
Cusp forms 256 96 160
Eisenstein series 64 0 64

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 32 q^{11} - 16 q^{14} + 96 q^{15} - 64 q^{18} - 48 q^{21} + 32 q^{22} - 32 q^{25} + 32 q^{35} - 64 q^{37} - 32 q^{39} - 48 q^{42} + 32 q^{44} - 32 q^{46} - 64 q^{49} + 64 q^{51} - 64 q^{53} + 32 q^{58} - 32 q^{60} - 96 q^{63} + 32 q^{65} - 64 q^{71} + 64 q^{74} - 16 q^{77} - 128 q^{78} + 96 q^{81} - 224 q^{85} + 32 q^{88} + 64 q^{91} - 32 q^{92} - 64 q^{93} + 64 q^{95} - 256 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(238, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
238.2.p.a 238.p 119.p $48$ $1.900$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
238.2.p.b 238.p 119.p $48$ $1.900$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(238, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(238, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 2}\)