↑

Properties

Label 1449.2.d
Level $1449$
Weight $2$
Character orbit 1449.d
Rep. character $\chi_{1449}(944,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1449.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(384\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1449, [\chi])\).

Total New Old
Modular forms 200 56 144
Cusp forms 184 56 128
Eisenstein series 16 0 16

Trace form

\( 56 q - 48 q^{4} + O(q^{10}) \) \( 56 q - 48 q^{4} + 32 q^{16} - 32 q^{22} + 88 q^{25} + 24 q^{28} + 48 q^{37} + 32 q^{43} - 64 q^{49} + 32 q^{58} - 32 q^{67} + 56 q^{70} - 80 q^{79} + 32 q^{85} + 40 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1449, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1449.2.d.a 1449.d 21.c $56$ $11.570$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1449, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1449, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)