Properties

Label 441.2.p
Level $441$
Weight $2$
Character orbit 441.p
Rep. character $\chi_{441}(80,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $3$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(441, [\chi])\).

Total New Old
Modular forms 144 28 116
Cusp forms 80 28 52
Eisenstein series 64 0 64

Trace form

\( 28 q + 16 q^{4} + O(q^{10}) \) \( 28 q + 16 q^{4} + 12 q^{10} - 28 q^{16} - 6 q^{19} - 22 q^{25} - 6 q^{31} + 34 q^{37} - 24 q^{40} - 68 q^{43} - 12 q^{46} - 4 q^{58} + 12 q^{61} + 32 q^{64} - 6 q^{67} - 6 q^{73} - 10 q^{79} + 36 q^{82} - 80 q^{85} - 4 q^{88} - 60 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
441.2.p.a 441.p 21.g $4$ $3.521$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 63.2.p.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-2\beta _{3})q^{5}-2\beta _{3}q^{8}+\cdots\)
441.2.p.b 441.p 21.g $8$ $3.521$ 8.0.\(\cdots\).5 \(\Q(\sqrt{-7}) \) 63.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+(2+\beta _{3}-2\beta _{4}+\beta _{6})q^{4}+\cdots\)
441.2.p.c 441.p 21.g $16$ $3.521$ \(\Q(\zeta_{48})\) None 441.2.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{48}-\zeta_{48}^{3}+\zeta_{48}^{5})q^{2}+(1-\zeta_{48}^{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(441, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)