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Properties

Label 2450.4.bd
Level $2450$
Weight $4$
Character orbit 2450.bd
Rep. character $\chi_{2450}(71,\cdot)$
Character field $\Q(\zeta_{35})$
Dimension $10080$
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.bd (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1225 \)
Character field: \(\Q(\zeta_{35})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 30336 10080 20256
Cusp forms 30144 10080 20064
Eisenstein series 192 0 192

Trace form

\( 10080 q + 1680 q^{4} - 16 q^{5} - 24 q^{6} - 4 q^{7} + 3780 q^{9} + O(q^{10}) \) \( 10080 q + 1680 q^{4} - 16 q^{5} - 24 q^{6} - 4 q^{7} + 3780 q^{9} + 24 q^{10} + 420 q^{11} - 378 q^{15} + 6720 q^{16} + 768 q^{17} + 456 q^{19} + 160 q^{20} + 48 q^{21} - 840 q^{22} + 84 q^{23} + 384 q^{24} + 140 q^{25} + 1248 q^{26} - 1344 q^{27} + 104 q^{28} - 168 q^{30} - 828 q^{31} + 1944 q^{33} - 272 q^{34} - 936 q^{35} + 15120 q^{36} - 672 q^{37} - 352 q^{38} - 560 q^{39} - 240 q^{40} - 80 q^{41} + 3300 q^{42} - 1232 q^{43} + 448 q^{44} - 2128 q^{45} + 856 q^{47} - 276 q^{49} - 112 q^{50} + 1176 q^{51} - 2800 q^{53} - 864 q^{54} + 2480 q^{55} - 7616 q^{57} + 3360 q^{58} - 1692 q^{59} + 2688 q^{60} + 580 q^{61} - 864 q^{62} - 5012 q^{63} + 26880 q^{64} - 1484 q^{65} + 32 q^{66} - 2016 q^{67} + 4096 q^{68} + 2592 q^{69} - 748 q^{70} + 13860 q^{71} + 5640 q^{73} + 10340 q^{75} + 1216 q^{76} + 5840 q^{77} + 3360 q^{78} + 672 q^{79} - 256 q^{80} + 30436 q^{81} + 2304 q^{82} - 7016 q^{83} + 1728 q^{84} - 8092 q^{85} - 840 q^{86} - 6068 q^{87} - 2016 q^{88} + 18264 q^{89} + 30736 q^{90} + 4128 q^{91} - 224 q^{92} + 5320 q^{93} - 1312 q^{94} + 4844 q^{95} - 384 q^{96} - 7956 q^{97} + 1744 q^{98} + 5040 q^{99} + O(q^{100}) \)

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

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