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Properties

Label 2450.4.u
Level $2450$
Weight $4$
Character orbit 2450.u
Rep. character $\chi_{2450}(361,\cdot)$
Character field $\Q(\zeta_{15})$
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.u (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 2400 q + 1200 q^{4} - 8 q^{5} - 48 q^{6} + 2700 q^{9} + O(q^{10}) \) \( 2400 q + 1200 q^{4} - 8 q^{5} - 48 q^{6} + 2700 q^{9} + 12 q^{10} - 84 q^{11} + 788 q^{15} + 4800 q^{16} + 288 q^{17} + 32 q^{18} + 76 q^{19} + 64 q^{20} + 528 q^{22} - 694 q^{23} - 384 q^{24} + 270 q^{25} - 1248 q^{26} - 1032 q^{27} + 192 q^{29} - 164 q^{30} - 414 q^{31} + 972 q^{33} - 544 q^{34} - 21600 q^{36} - 768 q^{37} - 176 q^{38} + 1184 q^{39} + 48 q^{40} - 1888 q^{41} + 2448 q^{43} + 224 q^{44} + 944 q^{45} + 1296 q^{46} + 440 q^{47} + 2720 q^{50} + 588 q^{51} + 3524 q^{53} + 864 q^{54} + 1036 q^{55} - 704 q^{57} - 1200 q^{58} + 216 q^{59} - 656 q^{60} + 1388 q^{61} + 864 q^{62} - 38400 q^{64} - 330 q^{65} + 1600 q^{66} + 848 q^{67} + 512 q^{68} - 5904 q^{69} + 2600 q^{71} + 128 q^{72} + 1344 q^{73} + 624 q^{74} + 934 q^{75} + 2432 q^{76} + 7040 q^{78} - 2000 q^{79} - 128 q^{80} + 22964 q^{81} + 1152 q^{82} + 5524 q^{83} + 16244 q^{85} + 168 q^{86} + 3932 q^{87} + 144 q^{88} - 1944 q^{89} + 2240 q^{90} - 5088 q^{92} + 1176 q^{93} + 1600 q^{94} + 4058 q^{95} + 384 q^{96} - 6852 q^{97} - 14512 q^{99} + O(q^{100}) \)

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

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