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Properties

Label 1449.2.be
Level $1449$
Weight $2$
Character orbit 1449.be
Rep. character $\chi_{1449}(530,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1449.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 400 120 280
Cusp forms 368 120 248
Eisenstein series 32 0 32

Trace form

\( 120 q + 64 q^{4} + 4 q^{7} + O(q^{10}) \) \( 120 q + 64 q^{4} + 4 q^{7} + 24 q^{10} - 72 q^{16} - 12 q^{19} + 32 q^{22} - 44 q^{25} - 64 q^{28} - 12 q^{31} - 4 q^{37} + 72 q^{40} + 24 q^{43} + 60 q^{49} - 56 q^{58} + 24 q^{61} - 32 q^{64} + 12 q^{67} - 8 q^{70} - 36 q^{73} - 12 q^{79} - 32 q^{85} + 72 q^{88} - 100 q^{91} - 120 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

The newforms in this space have not yet been added to the LMFDB.

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

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