Properties

Label 336.2.h
Level 336
Weight 2
Character orbit h
Rep. character \(\chi_{336}(239,\cdot)\)
Character field \(\Q\)
Dimension 12
Newforms 2
Sturm bound 128
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 336.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(128\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(336, [\chi])\).

Total New Old
Modular forms 76 12 64
Cusp forms 52 12 40
Eisenstein series 24 0 24

Trace form

\( 12q + 12q^{9} + O(q^{10}) \) \( 12q + 12q^{9} - 12q^{25} + 48q^{37} - 24q^{45} - 12q^{49} - 48q^{61} + 24q^{69} - 72q^{73} - 36q^{81} - 24q^{85} + 24q^{93} + 72q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
336.2.h.a \(4\) \(2.683\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
336.2.h.b \(8\) \(2.683\) 8.0.56070144.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{5}+\beta _{4}q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)