Properties

Label 29.6.a
Level $29$
Weight $6$
Character orbit 29.a
Rep. character $\chi_{29}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $2$
Sturm bound $15$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(15\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(29))\).

Total New Old
Modular forms 13 11 2
Cusp forms 11 11 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.

\(29\)Dim
\(+\)\(4\)
\(-\)\(7\)

Trace form

\( 11 q + 4 q^{2} - 2 q^{3} + 164 q^{4} - 36 q^{5} - 172 q^{6} - 24 q^{7} + 438 q^{8} + 725 q^{9} + 134 q^{10} + 982 q^{11} + 234 q^{12} - 52 q^{13} - 1240 q^{14} + 318 q^{15} - 172 q^{16} - 690 q^{17} - 2390 q^{18}+ \cdots + 467388 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(29))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 29
29.6.a.a 29.a 1.a $4$ $4.651$ 4.4.3257317.1 None 29.6.a.a \(0\) \(-28\) \(-68\) \(-208\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.a.b 29.a 1.a $7$ $4.651$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 29.6.a.b \(4\) \(26\) \(32\) \(184\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(4+\beta _{5})q^{3}+(23-3\beta _{1}+\cdots)q^{4}+\cdots\)