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Properties

Label 1050.2.bn
Level $1050$
Weight $2$
Character orbit 1050.bn
Rep. character $\chi_{1050}(131,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $640$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1050, [\chi])\).

Total New Old
Modular forms 1984 640 1344
Cusp forms 1856 640 1216
Eisenstein series 128 0 128

Trace form

\( 640 q - 80 q^{4} + 4 q^{7} + O(q^{10}) \) \( 640 q - 80 q^{4} + 4 q^{7} + 6 q^{10} - 44 q^{15} + 80 q^{16} + 8 q^{18} + 12 q^{21} + 16 q^{22} - 2 q^{25} + 6 q^{28} + 2 q^{30} + 18 q^{31} - 90 q^{33} + 8 q^{37} + 32 q^{39} + 6 q^{40} + 8 q^{42} + 64 q^{43} + 114 q^{45} - 12 q^{46} - 28 q^{49} - 12 q^{51} - 88 q^{57} - 28 q^{58} - 2 q^{60} - 14 q^{63} + 160 q^{64} + 48 q^{66} + 16 q^{67} + 150 q^{70} - 8 q^{72} - 168 q^{73} - 240 q^{75} - 16 q^{78} + 28 q^{79} + 44 q^{81} - 192 q^{82} + 18 q^{84} + 136 q^{85} - 36 q^{87} - 2 q^{88} + 52 q^{91} + 28 q^{93} - 48 q^{94} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1050, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)