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Properties

Label 2450.4.bp
Level $2450$
Weight $4$
Character orbit 2450.bp
Rep. character $\chi_{2450}(13,\cdot)$
Character field $\Q(\zeta_{140})$
Dimension $20160$
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.bp (of order \(140\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1225 \)
Character field: \(\Q(\zeta_{140})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 60672 20160 40512
Cusp forms 60288 20160 40128
Eisenstein series 384 0 384

Trace form

\( 20160 q + 4 q^{7} + O(q^{10}) \) \( 20160 q + 4 q^{7} - 84 q^{15} - 13440 q^{16} + 3584 q^{17} + 840 q^{22} + 56 q^{23} + 448 q^{25} + 224 q^{28} - 336 q^{30} - 2348 q^{35} - 30240 q^{36} - 672 q^{37} - 2976 q^{42} - 2128 q^{43} - 12992 q^{45} + 168 q^{47} - 448 q^{50} + 2800 q^{53} - 2184 q^{55} - 5824 q^{57} - 3360 q^{58} + 5740 q^{63} - 2520 q^{65} - 2016 q^{67} - 7512 q^{70} + 10164 q^{75} - 7752 q^{77} - 3360 q^{78} - 68040 q^{81} + 4760 q^{83} - 5760 q^{84} + 3640 q^{85} + 6636 q^{87} + 1344 q^{88} + 95200 q^{89} - 55776 q^{90} + 224 q^{92} - 13160 q^{93} - 3024 q^{95} - 4064 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)