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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
441.2.p.a \(4\) \(3.521\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-2\beta _{3})q^{5}-2\beta _{3}q^{8}+\cdots\)
441.2.p.b \(8\) \(3.521\) 8.0.\(\cdots\).5 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(2+\beta _{3}-2\beta _{4}+\beta _{6})q^{4}+\cdots\)
441.2.p.c \(16\) \(3.521\) \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{48}-\zeta_{48}^{3}+\zeta_{48}^{5})q^{2}+(1-\zeta_{48}^{2}+\cdots)q^{4}+\cdots\)

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

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