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Properties

Label 225.6.h
Level $225$
Weight $6$
Character orbit 225.h
Rep. character $\chi_{225}(46,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $244$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(225, [\chi])\).

Total New Old
Modular forms 616 252 364
Cusp forms 584 244 340
Eisenstein series 32 8 24

Trace form

\( 244 q - q^{2} - 947 q^{4} - 109 q^{5} - 50 q^{7} - 622 q^{8} + O(q^{10}) \) \( 244 q - q^{2} - 947 q^{4} - 109 q^{5} - 50 q^{7} - 622 q^{8} - 119 q^{10} - 244 q^{11} - 543 q^{13} - 2059 q^{14} - 17847 q^{16} + 1792 q^{17} - 1193 q^{19} + 3529 q^{20} + 4696 q^{22} + 3335 q^{23} - 14171 q^{25} + 14454 q^{26} - 24005 q^{28} + 4159 q^{29} + 11295 q^{31} + 16830 q^{32} + 24705 q^{34} + 4585 q^{35} - 7615 q^{37} - 12479 q^{38} + 80102 q^{40} - 21332 q^{41} + 39066 q^{43} - 16062 q^{44} + 2497 q^{46} - 58282 q^{47} + 516086 q^{49} + 20959 q^{50} - 186972 q^{52} + 41805 q^{53} - 16456 q^{55} + 68730 q^{56} + 251198 q^{58} + 49788 q^{59} + 22705 q^{61} - 261270 q^{62} - 414852 q^{64} - 230232 q^{65} + 71038 q^{67} + 123898 q^{68} + 72240 q^{70} + 44884 q^{71} + 49185 q^{73} + 86376 q^{74} - 61336 q^{76} + 347620 q^{77} + 28191 q^{79} + 459204 q^{80} + 540890 q^{82} - 305823 q^{83} - 9362 q^{85} - 221259 q^{86} - 54568 q^{88} + 123932 q^{89} + 182472 q^{91} + 153810 q^{92} + 21313 q^{94} + 44069 q^{95} + 390218 q^{97} - 315128 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

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