Properties

Label 237.2.h
Level $237$
Weight $2$
Character orbit 237.h
Rep. character $\chi_{237}(56,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $50$
Newform subspaces $2$
Sturm bound $53$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 237 = 3 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 237.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 237 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(53\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(237, [\chi])\).

Total New Old
Modular forms 58 58 0
Cusp forms 50 50 0
Eisenstein series 8 8 0

Trace form

\( 50 q - 3 q^{3} + 18 q^{4} - 3 q^{6} - 18 q^{7} + q^{9} + O(q^{10}) \) \( 50 q - 3 q^{3} + 18 q^{4} - 3 q^{6} - 18 q^{7} + q^{9} - 4 q^{10} - q^{13} - 4 q^{16} + 40 q^{18} - 10 q^{21} + 20 q^{22} - 6 q^{24} + 23 q^{25} - 84 q^{28} - 33 q^{30} + q^{31} + 18 q^{34} + q^{36} - 9 q^{37} - 6 q^{39} - 26 q^{40} - 31 q^{42} - 9 q^{43} - 10 q^{45} - 56 q^{46} + 66 q^{48} + 21 q^{49} - 20 q^{51} + 28 q^{52} - 87 q^{54} - 76 q^{55} - 3 q^{60} + 12 q^{63} + 84 q^{64} - 60 q^{66} + 10 q^{67} - 36 q^{70} + 59 q^{72} + 26 q^{73} + 12 q^{75} + 16 q^{76} + 27 q^{79} - 11 q^{81} - 60 q^{82} + 33 q^{84} + 36 q^{85} + 38 q^{87} + 10 q^{88} + 16 q^{90} - 78 q^{97} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(237, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
237.2.h.a 237.h 237.h $2$ $1.892$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-6\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(-4+2\zeta_{6})q^{7}+\cdots\)
237.2.h.b 237.h 237.h $48$ $1.892$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$