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Properties

Label 525.4.i
Level $525$
Weight $4$
Character orbit 525.i
Rep. character $\chi_{525}(151,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $152$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 525.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(525, [\chi])\).

Total New Old
Modular forms 504 152 352
Cusp forms 456 152 304
Eisenstein series 48 0 48

Trace form

\( 152 q + 2 q^{2} + 6 q^{3} - 314 q^{4} + 24 q^{6} - 24 q^{7} - 48 q^{8} - 684 q^{9} + O(q^{10}) \) \( 152 q + 2 q^{2} + 6 q^{3} - 314 q^{4} + 24 q^{6} - 24 q^{7} - 48 q^{8} - 684 q^{9} - 20 q^{11} + 72 q^{12} - 4 q^{13} + 322 q^{14} - 1210 q^{16} + 124 q^{17} + 18 q^{18} - 258 q^{19} + 132 q^{21} + 700 q^{22} - 196 q^{23} - 234 q^{24} - 34 q^{26} - 108 q^{27} + 934 q^{28} - 872 q^{29} - 568 q^{31} - 56 q^{32} + 114 q^{33} + 1752 q^{34} + 5652 q^{36} + 606 q^{37} - 294 q^{38} + 462 q^{39} - 1208 q^{41} - 408 q^{42} - 396 q^{43} - 20 q^{44} + 1316 q^{46} - 608 q^{47} - 816 q^{48} + 1080 q^{49} + 228 q^{51} + 1168 q^{52} - 1396 q^{53} - 108 q^{54} - 4572 q^{56} - 276 q^{57} - 2554 q^{58} + 1288 q^{59} - 1908 q^{61} + 2724 q^{62} + 162 q^{63} + 10612 q^{64} + 156 q^{66} - 770 q^{67} + 5016 q^{68} + 600 q^{69} + 4688 q^{71} + 216 q^{72} + 2322 q^{73} - 1910 q^{74} + 7152 q^{76} - 3108 q^{77} - 1980 q^{78} - 1772 q^{79} - 6156 q^{81} - 1288 q^{82} + 296 q^{83} - 3816 q^{84} - 1646 q^{86} + 1038 q^{87} - 1438 q^{88} + 3872 q^{89} - 4594 q^{91} + 7424 q^{92} - 894 q^{93} + 76 q^{94} - 3354 q^{96} + 396 q^{97} + 9052 q^{98} + 360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)