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 $1$

Related objects

Downloads

Learn more

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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
441.2.c.a 441.c 21.c $4$ $3.521$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 63.2.p.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{5}-2\beta _{1}q^{8}-2\beta _{2}q^{10}+\cdots\)
441.2.c.b 441.c 21.c $8$ $3.521$ \(\Q(\zeta_{16})\) None 441.2.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{16}-\zeta_{16}^{2})q^{2}+(-1+2\zeta_{16}^{3}+\cdots)q^{4}+\cdots\)

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

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