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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
441.4.c.a 441.c 21.c $16$ $26.020$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+(-4-\beta _{1})q^{4}+\beta _{10}q^{5}+\cdots\)
441.4.c.b 441.c 21.c $24$ $26.020$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

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