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Properties

Label 1449.2.bp
Level $1449$
Weight $2$
Character orbit 1449.bp
Rep. character $\chi_{1449}(181,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $780$
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.bp (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 2000 820 1180
Cusp forms 1840 780 1060
Eisenstein series 160 40 120

Trace form

\( 780 q + 16 q^{2} - 92 q^{4} - 11 q^{7} + 4 q^{8} + O(q^{10}) \) \( 780 q + 16 q^{2} - 92 q^{4} - 11 q^{7} + 4 q^{8} + 22 q^{11} + 11 q^{14} - 98 q^{16} - 8 q^{23} - 58 q^{25} + 33 q^{28} + 42 q^{29} - 18 q^{32} - 15 q^{35} - 66 q^{37} - 66 q^{43} + 55 q^{44} - 30 q^{46} - 31 q^{49} + 81 q^{50} + 22 q^{53} + 22 q^{56} - 51 q^{58} - 32 q^{64} - 132 q^{65} - 22 q^{67} + 2 q^{70} + 46 q^{71} + 11 q^{74} + 58 q^{77} - 110 q^{79} + 238 q^{85} - 22 q^{86} - 99 q^{88} + 168 q^{92} - 68 q^{95} + 53 q^{98} + O(q^{100}) \)

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

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