↑

Properties

Label 1071.2.n
Level $1071$
Weight $2$
Character orbit 1071.n
Rep. character $\chi_{1071}(64,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $92$
Newform subspaces $4$
Sturm bound $288$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1071.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1071, [\chi])\).

Total New Old
Modular forms 304 92 212
Cusp forms 272 92 180
Eisenstein series 32 0 32

Trace form

\( 92 q - 96 q^{4} - 8 q^{5} + O(q^{10}) \) \( 92 q - 96 q^{4} - 8 q^{5} + 12 q^{10} - 4 q^{11} + 16 q^{13} + 120 q^{16} - 12 q^{17} + 20 q^{20} - 4 q^{22} + 24 q^{29} - 12 q^{31} - 12 q^{34} - 16 q^{35} - 4 q^{37} + 32 q^{38} - 16 q^{40} + 64 q^{41} - 36 q^{44} + 40 q^{46} - 40 q^{47} - 124 q^{50} - 64 q^{52} + 40 q^{55} - 16 q^{58} - 40 q^{61} + 32 q^{62} - 104 q^{64} + 40 q^{65} + 32 q^{67} + 72 q^{68} + 8 q^{71} - 16 q^{73} - 20 q^{74} + 28 q^{79} + 4 q^{80} - 24 q^{82} + 40 q^{85} - 12 q^{86} - 40 q^{88} - 48 q^{89} + 4 q^{91} + 64 q^{92} - 68 q^{95} - 40 q^{97} + 8 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1071, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1071.2.n.a 1071.n 17.c $12$ $8.552$ 12.0.\(\cdots\).1 None 357.2.k.a \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{10}q^{2}+(1-\beta _{2}+\beta _{7}-\beta _{8})q^{4}+\cdots\)
1071.2.n.b 1071.n 17.c $20$ $8.552$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 357.2.k.b \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{7}+\beta _{8})q^{4}+(\beta _{10}+\cdots)q^{5}+\cdots\)
1071.2.n.c 1071.n 17.c $20$ $8.552$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 119.2.g.a \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{12}+\beta _{13})q^{4}+(1+\cdots)q^{5}+\cdots\)
1071.2.n.d 1071.n 17.c $40$ $8.552$ None 1071.2.n.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1071, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1071, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)