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Properties

Label 2450.4.p
Level $2450$
Weight $4$
Character orbit 2450.p
Rep. character $\chi_{2450}(607,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $720$
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.p (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 5232 720 4512
Cusp forms 4848 720 4128
Eisenstein series 384 0 384

Trace form

\( 720 q + O(q^{10}) \) \( 720 q + 120 q^{11} + 5760 q^{16} + 288 q^{17} + 32 q^{18} + 912 q^{22} - 532 q^{23} + 912 q^{26} - 1056 q^{31} - 1956 q^{33} - 28416 q^{36} - 768 q^{37} - 528 q^{38} + 2784 q^{43} + 1792 q^{46} + 1464 q^{47} - 2016 q^{51} - 360 q^{53} + 2016 q^{57} + 144 q^{58} + 2808 q^{61} - 2864 q^{67} + 1152 q^{68} - 5824 q^{71} + 128 q^{72} - 5616 q^{73} - 7040 q^{78} + 44856 q^{81} + 864 q^{82} + 1200 q^{86} + 15732 q^{87} + 1824 q^{88} + 4256 q^{92} - 2344 q^{93} - 768 q^{96} + O(q^{100}) \)

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

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