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Properties

Label 1.68.a
Level $1$
Weight $68$
Character orbit 1.a
Rep. character $\chi_{1}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $1$
Sturm bound $5$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 68 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{68}(\Gamma_0(1))\).

Total New Old
Modular forms 6 6 0
Cusp forms 5 5 0
Eisenstein series 1 1 0

Trace form

\( 5 q + 5554901256 q^{2} + 34\!\cdots\!72 q^{3} + 35\!\cdots\!40 q^{4} + 33\!\cdots\!50 q^{5} + 14\!\cdots\!60 q^{6} + 33\!\cdots\!56 q^{7} + 32\!\cdots\!80 q^{8} + 27\!\cdots\!85 q^{9} - 52\!\cdots\!00 q^{10}+ \cdots + 16\!\cdots\!20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{68}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1.68.a.a 1.a 1.a $5$ $28.429$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1.68.a.a \(5554901256\) \(34\!\cdots\!72\) \(33\!\cdots\!50\) \(33\!\cdots\!56\) $+$ $\mathrm{SU}(2)$ \(q+(1110980251-\beta _{1})q^{2}+(688672053797479+\cdots)q^{3}+\cdots\)