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Properties

Label 1035.2.j
Level $1035$
Weight $2$
Character orbit 1035.j
Rep. character $\chi_{1035}(323,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $2$
Sturm bound $288$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1035.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1035, [\chi])\).

Total New Old
Modular forms 304 88 216
Cusp forms 272 88 184
Eisenstein series 32 0 32

Trace form

\( 88 q + 16 q^{7} + O(q^{10}) \) \( 88 q + 16 q^{7} + 16 q^{10} + 8 q^{13} - 88 q^{16} - 48 q^{22} + 48 q^{28} + 32 q^{31} + 24 q^{37} - 56 q^{40} + 64 q^{43} + 8 q^{52} + 48 q^{55} - 88 q^{58} - 32 q^{61} - 32 q^{67} + 64 q^{70} - 24 q^{73} - 32 q^{76} - 8 q^{82} - 16 q^{85} - 48 q^{88} + 96 q^{91} + 136 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1035, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1035.2.j.a 1035.j 15.e $44$ $8.265$ None 1035.2.j.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$
1035.2.j.b 1035.j 15.e $44$ $8.265$ None 1035.2.j.b \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1035, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1035, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)