Properties

Label 441.4.c
Level $441$
Weight $4$
Character orbit 441.c
Rep. character $\chi_{441}(440,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $2$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 184 40 144
Cusp forms 152 40 112
Eisenstein series 32 0 32

Trace form

\( 40q - 160q^{4} + O(q^{10}) \) \( 40q - 160q^{4} + 520q^{16} + 1152q^{22} + 352q^{25} + 1528q^{37} + 1576q^{43} - 1104q^{46} - 696q^{58} + 2072q^{64} - 3304q^{67} + 4832q^{79} + 8640q^{85} - 8664q^{88} + O(q^{100}) \)

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.c.a \(16\) \(26.020\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(-4-\beta _{1})q^{4}+\beta _{10}q^{5}+\cdots\)
441.4.c.b \(24\) \(26.020\) None \(0\) \(0\) \(0\) \(0\)

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

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