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Properties

Label 272.3.d
Level $272$
Weight $3$
Character orbit 272.d
Rep. character $\chi_{272}(239,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $108$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 272.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(108\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(272, [\chi])\).

Total New Old
Modular forms 78 16 62
Cusp forms 66 16 50
Eisenstein series 12 0 12

Trace form

\( 16 q - 48 q^{9} + 16 q^{13} + 32 q^{25} - 144 q^{29} + 144 q^{33} + 80 q^{37} - 48 q^{41} + 288 q^{45} - 224 q^{49} - 144 q^{53} - 48 q^{57} - 112 q^{61} + 48 q^{65} - 48 q^{69} + 256 q^{73} - 144 q^{77}+ \cdots + 208 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(272, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
272.3.d.a 272.d 4.b $4$ $7.411$ 4.0.2312.1 None 272.3.d.a \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(3+\beta _{2})q^{5}+\beta _{3}q^{7}+(-5+\cdots)q^{9}+\cdots\)
272.3.d.b 272.d 4.b $12$ $7.411$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 272.3.d.b \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+\beta _{4}q^{7}+(-2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(272, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(272, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)