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Properties

Label 1449.2.bz
Level $1449$
Weight $2$
Character orbit 1449.bz
Rep. character $\chi_{1449}(100,\cdot)$
Character field $\Q(\zeta_{33})$
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.bz (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
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

\( 1560 q + 7 q^{2} + 65 q^{4} + 15 q^{5} - 20 q^{7} + 56 q^{8} + O(q^{10}) \) \( 1560 q + 7 q^{2} + 65 q^{4} + 15 q^{5} - 20 q^{7} + 56 q^{8} - 21 q^{10} + 11 q^{11} - 36 q^{13} + 10 q^{14} + 83 q^{16} + 13 q^{17} - 13 q^{19} + 108 q^{20} - 96 q^{22} + 33 q^{23} + 89 q^{25} + 11 q^{26} - 144 q^{28} + 80 q^{29} - 7 q^{31} + 27 q^{32} + 20 q^{34} + 50 q^{35} - 61 q^{37} + 107 q^{38} - 11 q^{40} + 40 q^{41} + 32 q^{43} + 116 q^{44} - 11 q^{46} + 10 q^{47} + 24 q^{49} - 130 q^{50} - 171 q^{52} - 3 q^{53} - 48 q^{55} + 19 q^{56} + 30 q^{58} + 45 q^{59} - 79 q^{61} + 92 q^{62} - 136 q^{64} + 106 q^{65} - 21 q^{67} - 214 q^{68} - 158 q^{70} + 12 q^{71} - 9 q^{73} + 32 q^{74} - 44 q^{76} - 69 q^{77} + 19 q^{79} - 20 q^{80} - 127 q^{82} + 56 q^{83} + 92 q^{85} - 9 q^{86} + 88 q^{88} - 11 q^{89} - 22 q^{91} + 242 q^{92} - 34 q^{94} + 96 q^{95} - 76 q^{97} + 44 q^{98} + O(q^{100}) \)

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

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