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Properties

Label 2450.4.v
Level $2450$
Weight $4$
Character orbit 2450.v
Rep. character $\chi_{2450}(97,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2400$
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.v (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 10208 2400 7808
Cusp forms 9952 2400 7552
Eisenstein series 256 0 256

Trace form

\( 2400 q + O(q^{10}) \) \( 2400 q + 504 q^{15} + 9600 q^{16} - 32 q^{18} - 1488 q^{22} - 1144 q^{23} + 592 q^{25} - 320 q^{29} + 48 q^{30} + 21600 q^{36} - 240 q^{37} - 4880 q^{39} - 1520 q^{43} - 448 q^{50} - 5760 q^{53} + 5824 q^{57} + 1872 q^{58} + 704 q^{60} - 4104 q^{65} - 160 q^{67} - 128 q^{72} - 1504 q^{78} + 48600 q^{81} + 6504 q^{85} + 192 q^{88} + 2464 q^{92} + 14800 q^{93} - 7248 q^{95} + O(q^{100}) \)

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

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