Properties

Label 441.4.p
Level $441$
Weight $4$
Character orbit 441.p
Rep. character $\chi_{441}(80,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $4$
Sturm bound $224$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(224\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(441, [\chi])\).

Total New Old
Modular forms 368 80 288
Cusp forms 304 80 224
Eisenstein series 64 0 64

Trace form

\( 80q + 160q^{4} + O(q^{10}) \) \( 80q + 160q^{4} + 72q^{10} - 520q^{16} + 612q^{19} - 216q^{22} - 1108q^{25} - 1128q^{31} + 404q^{37} + 3204q^{40} + 1304q^{43} + 2364q^{46} - 4452q^{52} + 5232q^{58} + 1632q^{61} - 12488q^{64} - 1148q^{67} - 4068q^{73} - 464q^{79} + 10188q^{82} + 11232q^{85} + 1104q^{88} + 2916q^{94} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
441.4.p.a \(8\) \(26.020\) 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{4}q^{2}+(\beta _{2}-\beta _{5})q^{5}+(2^{4}\beta _{3}+2^{4}\beta _{4}+\cdots)q^{8}+\cdots\)
441.4.p.b \(8\) \(26.020\) 8.0.\(\cdots\).5 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(8+5\beta _{1}-8\beta _{2}+5\beta _{4})q^{4}+\cdots\)
441.4.p.c \(16\) \(26.020\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(4+\beta _{2}-4\beta _{3}+\beta _{9})q^{4}+\cdots\)
441.4.p.d \(48\) \(26.020\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

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