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Properties

Label 1449.2.cv
Level $1449$
Weight $2$
Character orbit 1449.cv
Rep. character $\chi_{1449}(10,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $1560$
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.cv (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 4000 1640 2360
Cusp forms 3680 1560 2120
Eisenstein series 320 80 240

Trace form

\( 1560 q + 11 q^{2} + 65 q^{4} + 33 q^{5} - 22 q^{7} + 32 q^{8} + O(q^{10}) \) \( 1560 q + 11 q^{2} + 65 q^{4} + 33 q^{5} - 22 q^{7} + 32 q^{8} - 33 q^{10} + 11 q^{11} + 22 q^{14} + 83 q^{16} + 33 q^{17} - 33 q^{19} + 17 q^{23} + 37 q^{25} + 105 q^{26} + 66 q^{28} + 24 q^{29} - 33 q^{31} - 9 q^{32} + 66 q^{35} + 33 q^{37} + 33 q^{38} - 33 q^{40} - 132 q^{43} - 88 q^{44} + 3 q^{46} + 18 q^{47} + 88 q^{49} + 186 q^{50} - 105 q^{52} + 11 q^{53} + 11 q^{56} - 24 q^{58} + 15 q^{59} - 33 q^{61} - 136 q^{64} - 66 q^{65} - 11 q^{67} - 146 q^{70} + 44 q^{71} - 39 q^{73} + 22 q^{74} - 13 q^{77} - 55 q^{79} + 330 q^{80} - 105 q^{82} - 244 q^{85} - 11 q^{86} + 198 q^{88} + 33 q^{89} - 30 q^{92} + 180 q^{94} + 122 q^{95} - 56 q^{98} + O(q^{100}) \)

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

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