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Properties

Label 2450.2.j
Level $2450$
Weight $2$
Character orbit 2450.j
Rep. character $\chi_{2450}(949,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2450.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2450, [\chi])\).

Total New Old
Modular forms 936 120 816
Cusp forms 744 120 624
Eisenstein series 192 0 192

Trace form

\( 120 q + 60 q^{4} - 16 q^{6} + 72 q^{9} + O(q^{10}) \) \( 120 q + 60 q^{4} - 16 q^{6} + 72 q^{9} - 16 q^{11} - 60 q^{16} - 4 q^{19} - 8 q^{24} + 16 q^{26} + 24 q^{29} + 12 q^{31} + 16 q^{34} + 144 q^{36} + 40 q^{39} + 8 q^{41} + 16 q^{44} + 32 q^{46} - 28 q^{51} - 20 q^{54} - 4 q^{59} - 16 q^{61} - 120 q^{64} + 8 q^{71} + 36 q^{74} - 8 q^{76} + 52 q^{79} - 124 q^{81} - 24 q^{86} - 16 q^{89} + 4 q^{94} + 8 q^{96} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)