Properties

Label 3.14.a
Level $3$
Weight $14$
Character orbit 3.a
Rep. character $\chi_{3}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $4$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(3))\).

Total New Old
Modular forms 5 3 2
Cusp forms 3 3 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)Dim
\(+\)\(1\)
\(-\)\(2\)

Trace form

\( 3 q - 66 q^{2} + 729 q^{3} + 12468 q^{4} + 10506 q^{5} - 30618 q^{6} + 214080 q^{7} - 1830552 q^{8} + 1594323 q^{9} + 3799764 q^{10} - 10510500 q^{11} + 20823156 q^{12} + 25582218 q^{13} - 124741392 q^{14}+ \cdots - 5585710630500 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3
3.14.a.a 3.a 1.a $1$ $3.217$ \(\Q\) None 3.14.a.a \(-12\) \(-729\) \(-30210\) \(235088\) $+$ $\mathrm{SU}(2)$ \(q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots\)
3.14.a.b 3.a 1.a $2$ $3.217$ \(\Q(\sqrt{1969}) \) None 3.14.a.b \(-54\) \(1458\) \(40716\) \(-21008\) $-$ $\mathrm{SU}(2)$ \(q+(-3^{3}-\beta )q^{2}+3^{6}q^{3}+(10258+54\beta )q^{4}+\cdots\)