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Properties

Label 2450.4.bi
Level $2450$
Weight $4$
Character orbit 2450.bi
Rep. character $\chi_{2450}(117,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $4800$
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.bi (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 20416 4800 15616
Cusp forms 19904 4800 15104
Eisenstein series 512 0 512

Trace form

\( 4800 q + 48 q^{5} + O(q^{10}) \) \( 4800 q + 48 q^{5} - 72 q^{10} - 504 q^{15} - 9600 q^{16} + 288 q^{17} + 32 q^{18} - 1968 q^{22} + 1228 q^{23} + 80 q^{25} - 640 q^{29} - 552 q^{30} - 1956 q^{33} + 43200 q^{36} - 768 q^{37} - 528 q^{38} + 4880 q^{39} + 3344 q^{43} - 2832 q^{45} + 1464 q^{47} + 448 q^{50} + 4080 q^{53} + 896 q^{57} + 144 q^{58} + 4920 q^{59} - 704 q^{60} + 324 q^{65} - 2864 q^{67} - 4608 q^{68} + 128 q^{72} - 5616 q^{73} - 30288 q^{75} - 7040 q^{78} + 768 q^{80} - 48600 q^{81} - 3456 q^{82} + 2088 q^{85} + 15732 q^{87} + 1824 q^{88} + 40800 q^{89} + 4256 q^{92} - 6904 q^{93} + 2712 q^{95} + O(q^{100}) \)

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

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