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Properties

Label 2450.4.j
Level $2450$
Weight $4$
Character orbit 2450.j
Rep. character $\chi_{2450}(949,\cdot)$
Character field $\Q(\zeta_{6})$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 360 q + 720 q^{4} + 64 q^{6} + 1464 q^{9} + O(q^{10}) \) \( 360 q + 720 q^{4} + 64 q^{6} + 1464 q^{9} - 52 q^{11} - 2880 q^{16} - 64 q^{19} + 128 q^{24} - 160 q^{26} - 2184 q^{29} - 308 q^{31} - 544 q^{34} + 11712 q^{36} - 144 q^{39} + 656 q^{41} + 208 q^{44} + 752 q^{46} - 3356 q^{51} + 2216 q^{54} + 1636 q^{59} - 1400 q^{61} - 23040 q^{64} - 1600 q^{66} + 104 q^{69} + 5264 q^{71} - 1032 q^{74} - 512 q^{76} - 7356 q^{79} - 11908 q^{81} + 1136 q^{86} + 7332 q^{89} + 5608 q^{94} - 512 q^{96} - 34984 q^{99} + O(q^{100}) \)

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

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