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Properties

Label 28.9.b
Level $28$
Weight $9$
Character orbit 28.b
Rep. character $\chi_{28}(13,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 28.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(28, [\chi])\).

Total New Old
Modular forms 35 6 29
Cusp forms 29 6 23
Eisenstein series 6 0 6

Trace form

\( 6 q + 2166 q^{7} - 18234 q^{9} + O(q^{10}) \) \( 6 q + 2166 q^{7} - 18234 q^{9} + 24492 q^{11} - 153408 q^{15} - 33216 q^{21} - 11604 q^{23} - 678714 q^{25} + 1264332 q^{29} - 1314816 q^{35} + 3184332 q^{37} + 5634240 q^{39} - 7783380 q^{43} + 2719110 q^{49} + 6877824 q^{51} - 8340660 q^{53} - 17950848 q^{57} - 66574602 q^{63} + 84095232 q^{65} + 16579500 q^{67} - 62088852 q^{71} - 61390452 q^{77} + 186114540 q^{79} + 131284998 q^{81} - 263210880 q^{85} - 179101056 q^{91} + 638128512 q^{93} + 85912896 q^{95} - 595897812 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(28, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
28.9.b.a 28.b 7.b $6$ $11.407$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(2166\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-3\beta _{1}-\beta _{2})q^{5}+(19^{2}-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)