Properties

Label 441.2.c
Level $441$
Weight $2$
Character orbit 441.c
Rep. character $\chi_{441}(440,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
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 72 12 60
Cusp forms 40 12 28
Eisenstein series 32 0 32

Trace form

\( 12q - 8q^{4} + O(q^{10}) \) \( 12q - 8q^{4} + 8q^{16} - 24q^{22} + 44q^{25} - 36q^{37} - 36q^{43} - 48q^{46} + 64q^{58} + 24q^{64} + 44q^{67} - 12q^{79} - 16q^{85} - 32q^{88} + O(q^{100}) \)

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.c.a \(4\) \(3.521\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{5}-2\beta _{1}q^{8}-2\beta _{2}q^{10}+\cdots\)
441.2.c.b \(8\) \(3.521\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{16}-\zeta_{16}^{2})q^{2}+(-1+2\zeta_{16}^{3}+\cdots)q^{4}+\cdots\)

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

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