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Properties

Label 1449.1.bq
Level $1449$
Weight $1$
Character orbit 1449.bq
Rep. character $\chi_{1449}(55,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $30$
Newform subspaces $2$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1449.bq (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1449, [\chi])\).

Total New Old
Modular forms 140 50 90
Cusp forms 60 30 30
Eisenstein series 80 20 60

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 30 0 0 0

Trace form

\( 30 q + 2 q^{2} - q^{4} + q^{7} + 4 q^{8} + O(q^{10}) \) \( 30 q + 2 q^{2} - q^{4} + q^{7} + 4 q^{8} + 2 q^{11} + 2 q^{14} - 18 q^{16} - 4 q^{22} + q^{23} - 3 q^{25} - 5 q^{28} + 2 q^{29} - 5 q^{32} + 2 q^{37} + 2 q^{43} - 5 q^{44} - 2 q^{46} - 3 q^{49} - 9 q^{50} + 2 q^{53} + 4 q^{56} + 29 q^{58} - 5 q^{64} - 6 q^{67} + 2 q^{71} - 7 q^{74} - 9 q^{77} - 6 q^{79} + 4 q^{86} - 19 q^{88} + 3 q^{92} - 9 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1449, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1449.1.bq.a 1449.bq 161.l $10$ $0.723$ \(\Q(\zeta_{22})\) $D_{11}$ \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(-1\) \(q+(\zeta_{22}^{3}-\zeta_{22}^{10})q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{6}+\cdots)q^{4}+\cdots\)
1449.1.bq.b 1449.bq 161.l $20$ $0.723$ \(\Q(\zeta_{44})\) $D_{22}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(2\) \(q+(-\zeta_{44}^{5}-\zeta_{44}^{7})q^{2}+(\zeta_{44}^{10}+\zeta_{44}^{12}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1449, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1449, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)