↑

Properties

Label 882.4.k
Level $882$
Weight $4$
Character orbit 882.k
Rep. character $\chi_{882}(215,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $4$
Sturm bound $672$
Trace bound $22$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(672\)
Trace bound: \(22\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(882, [\chi])\).

Total New Old
Modular forms 1072 80 992
Cusp forms 944 80 864
Eisenstein series 128 0 128

Trace form

\( 80 q + 160 q^{4} + O(q^{10}) \) \( 80 q + 160 q^{4} - 72 q^{10} - 640 q^{16} - 684 q^{19} - 240 q^{22} - 1060 q^{25} + 1248 q^{31} + 548 q^{37} - 288 q^{40} - 1528 q^{43} - 1344 q^{46} + 336 q^{52} - 600 q^{58} - 3264 q^{61} - 5120 q^{64} + 2692 q^{67} + 3132 q^{73} + 2296 q^{79} + 864 q^{82} - 3360 q^{85} - 480 q^{88} + 2160 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
882.4.k.a 882.k 21.g $16$ $52.040$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{8}q^{2}+(4-4\beta _{1})q^{4}+(2\beta _{4}+\beta _{8}+\cdots)q^{5}+\cdots\)
882.4.k.b 882.k 21.g $16$ $52.040$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{48}q^{2}+4\zeta_{48}^{3}q^{4}+(3\zeta_{48}^{4}+4\zeta_{48}^{8}+\cdots)q^{5}+\cdots\)
882.4.k.c 882.k 21.g $16$ $52.040$ 16.0.\(\cdots\).8 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+4\beta _{2}q^{4}+(-\beta _{4}+\beta _{6})q^{5}+\cdots\)
882.4.k.d 882.k 21.g $32$ $52.040$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)