↑

Properties

Label 450.4.l
Level $450$
Weight $4$
Character orbit 450.l
Rep. character $\chi_{450}(19,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $152$
Sturm bound $360$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 450.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(450, [\chi])\).

Total New Old
Modular forms 1112 152 960
Cusp forms 1048 152 896
Eisenstein series 64 0 64

Trace form

\( 152 q + 152 q^{4} + 34 q^{5} + O(q^{10}) \) \( 152 q + 152 q^{4} + 34 q^{5} - 4 q^{10} - 62 q^{11} - 56 q^{14} - 608 q^{16} + 320 q^{17} - 34 q^{19} - 96 q^{20} + 360 q^{22} - 370 q^{23} - 348 q^{25} - 440 q^{26} + 120 q^{28} - 358 q^{29} + 342 q^{31} + 220 q^{34} + 1424 q^{35} + 350 q^{37} + 16 q^{40} + 560 q^{41} - 312 q^{44} + 464 q^{46} - 2760 q^{47} - 7932 q^{49} - 576 q^{50} - 2550 q^{53} - 552 q^{55} + 224 q^{56} - 450 q^{59} - 950 q^{61} - 720 q^{62} + 2432 q^{64} + 778 q^{65} - 2340 q^{67} + 3728 q^{70} + 448 q^{71} + 600 q^{73} + 3336 q^{74} + 416 q^{76} + 6560 q^{77} - 40 q^{79} - 96 q^{80} + 4330 q^{83} - 2782 q^{85} + 1028 q^{86} + 1680 q^{88} - 5456 q^{89} - 1276 q^{91} - 1280 q^{92} + 848 q^{94} - 6156 q^{95} + 3570 q^{97} + 3280 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)