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Properties

Label 525.6.bg
Level $525$
Weight $6$
Character orbit 525.bg
Rep. character $\chi_{525}(16,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1600$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 525.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(525, [\chi])\).

Total New Old
Modular forms 3232 1600 1632
Cusp forms 3168 1600 1568
Eisenstein series 64 0 64

Trace form

\( 1600 q + 3200 q^{4} - 22 q^{5} - 288 q^{6} - 312 q^{7} - 1476 q^{8} + 16200 q^{9} + O(q^{10}) \) \( 1600 q + 3200 q^{4} - 22 q^{5} - 288 q^{6} - 312 q^{7} - 1476 q^{8} + 16200 q^{9} + 782 q^{10} - 474 q^{11} - 2748 q^{14} - 396 q^{15} + 51200 q^{16} - 2292 q^{17} + 5776 q^{19} + 6152 q^{20} + 8512 q^{22} - 13188 q^{23} - 27648 q^{24} - 5420 q^{25} + 19740 q^{28} - 17016 q^{29} + 22176 q^{30} + 33030 q^{31} - 15744 q^{32} + 14148 q^{33} - 61600 q^{34} - 12176 q^{35} - 518400 q^{36} - 18524 q^{37} + 43222 q^{38} - 15882 q^{40} + 27684 q^{41} - 11916 q^{42} + 238264 q^{43} + 20224 q^{44} - 1782 q^{45} + 34388 q^{46} - 17684 q^{47} - 89568 q^{48} - 30184 q^{49} - 379388 q^{50} + 226914 q^{52} - 3540 q^{53} + 11664 q^{54} - 87344 q^{55} + 116100 q^{56} + 10224 q^{57} - 120764 q^{58} - 101256 q^{59} + 30906 q^{60} + 36620 q^{61} + 188784 q^{62} + 40986 q^{63} - 2049364 q^{64} - 22930 q^{65} + 69696 q^{66} - 148924 q^{67} - 96732 q^{68} - 152352 q^{69} - 181110 q^{70} - 10912 q^{71} + 59778 q^{72} + 95764 q^{73} - 239412 q^{74} + 9432 q^{75} + 1865144 q^{76} + 629212 q^{77} + 269424 q^{78} + 58164 q^{79} - 219276 q^{80} + 1312200 q^{81} - 259652 q^{82} - 192752 q^{83} + 47088 q^{84} - 1126148 q^{85} + 201696 q^{86} - 175536 q^{87} + 70062 q^{88} + 305856 q^{90} - 121306 q^{91} + 158468 q^{92} + 9504 q^{93} + 432576 q^{94} - 770142 q^{95} + 109278 q^{96} - 1140804 q^{97} + 1221792 q^{98} - 51192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(525, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)