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Properties

Label 1449.2.i
Level $1449$
Weight $2$
Character orbit 1449.i
Rep. character $\chi_{1449}(415,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $148$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 400 148 252
Cusp forms 368 148 220
Eisenstein series 32 0 32

Trace form

\( 148 q - 76 q^{4} + 10 q^{7} - 12 q^{8} + O(q^{10}) \) \( 148 q - 76 q^{4} + 10 q^{7} - 12 q^{8} + 2 q^{10} + 4 q^{11} + 16 q^{13} + 16 q^{14} - 72 q^{16} - 2 q^{17} - 10 q^{19} + 8 q^{20} + 24 q^{22} - 90 q^{25} - 4 q^{26} + 2 q^{28} - 20 q^{29} + 22 q^{32} - 64 q^{34} - 10 q^{35} + 10 q^{37} + 10 q^{38} - 36 q^{41} - 28 q^{43} + 2 q^{44} + 24 q^{47} + 24 q^{49} + 12 q^{50} - 28 q^{52} - 10 q^{53} - 12 q^{55} - 8 q^{56} + 30 q^{58} + 34 q^{59} + 28 q^{61} + 24 q^{62} + 156 q^{64} - 14 q^{65} + 22 q^{67} - 28 q^{68} + 58 q^{70} + 8 q^{71} - 22 q^{73} - 22 q^{74} - 64 q^{76} + 20 q^{77} - 14 q^{79} - 84 q^{80} - 12 q^{82} + 12 q^{83} + 84 q^{85} + 22 q^{86} + 22 q^{88} - 10 q^{89} - 26 q^{91} - 56 q^{94} - 4 q^{95} + 30 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1449, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)