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Properties

Label 2450.4.g
Level $2450$
Weight $4$
Character orbit 2450.g
Rep. character $\chi_{2450}(293,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $360$
Sturm bound $1680$

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Defining parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2450.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Sturm bound: \(1680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2450, [\chi])\).

Total New Old
Modular forms 2616 360 2256
Cusp forms 2424 360 2064
Eisenstein series 192 0 192

Trace form

\( 360 q + O(q^{10}) \) \( 360 q + 48 q^{11} - 5760 q^{16} - 32 q^{18} - 48 q^{22} + 616 q^{23} - 13536 q^{36} - 240 q^{37} - 960 q^{43} + 3584 q^{46} + 6048 q^{51} - 1320 q^{53} + 4704 q^{57} + 1872 q^{58} - 160 q^{67} - 7616 q^{71} - 128 q^{72} - 1504 q^{78} - 38472 q^{81} + 4512 q^{86} + 192 q^{88} + 2464 q^{92} + 10240 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)