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Properties

Label 1450.2.bn
Level $1450$
Weight $2$
Character orbit 1450.bn
Rep. character $\chi_{1450}(3,\cdot)$
Character field $\Q(\zeta_{140})$
Dimension $3600$
Sturm bound $450$

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Defining parameters

Level: \( N \) \(=\) \( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1450.bn (of order \(140\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 725 \)
Character field: \(\Q(\zeta_{140})\)
Sturm bound: \(450\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1450, [\chi])\).

Total New Old
Modular forms 10992 3600 7392
Cusp forms 10608 3600 7008
Eisenstein series 384 0 384

Trace form

\( 3600 q - 150 q^{4} + 150 q^{9} + O(q^{10}) \) \( 3600 q - 150 q^{4} + 150 q^{9} + 10 q^{10} - 38 q^{13} + 150 q^{16} + 40 q^{19} - 30 q^{25} + 60 q^{26} - 300 q^{27} + 40 q^{29} - 20 q^{31} + 4 q^{33} + 40 q^{35} - 150 q^{36} - 42 q^{37} - 28 q^{38} - 10 q^{40} - 50 q^{41} + 32 q^{42} + 120 q^{43} + 40 q^{45} - 36 q^{47} - 40 q^{50} - 18 q^{52} - 208 q^{53} - 32 q^{55} - 48 q^{57} - 2 q^{58} - 92 q^{60} + 470 q^{61} + 136 q^{63} - 150 q^{64} + 16 q^{65} + 16 q^{67} - 48 q^{70} - 52 q^{73} + 208 q^{75} + 244 q^{77} + 152 q^{78} - 80 q^{79} + 150 q^{81} + 34 q^{82} + 56 q^{83} + 60 q^{84} - 8 q^{85} - 76 q^{87} + 20 q^{89} + 178 q^{90} - 52 q^{93} + 456 q^{95} + 12 q^{97} + 366 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)