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Properties

Label 225.6.e
Level $225$
Weight $6$
Character orbit 225.e
Rep. character $\chi_{225}(76,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $184$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(180\)

Dimensions

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

Total New Old
Modular forms 312 196 116
Cusp forms 288 184 104
Eisenstein series 24 12 12

Trace form

\( 184 q + 5 q^{2} - 10 q^{3} - 1423 q^{4} - 57 q^{6} + 30 q^{7} - 870 q^{8} + 348 q^{9} + O(q^{10}) \) \( 184 q + 5 q^{2} - 10 q^{3} - 1423 q^{4} - 57 q^{6} + 30 q^{7} - 870 q^{8} + 348 q^{9} - 906 q^{11} + 2050 q^{12} - 180 q^{13} - 126 q^{14} - 21219 q^{16} - 3280 q^{17} + 1700 q^{18} + 960 q^{19} - 1428 q^{21} + 885 q^{22} - 2430 q^{23} + 1743 q^{24} - 10560 q^{26} - 15910 q^{27} - 5820 q^{28} - 12852 q^{29} - 3304 q^{31} + 15445 q^{32} - 1340 q^{33} - 2597 q^{34} - 14133 q^{36} + 4860 q^{37} + 6965 q^{38} - 27738 q^{39} - 1590 q^{41} - 19080 q^{42} - 6090 q^{43} + 31170 q^{44} - 45976 q^{46} + 31280 q^{47} - 68135 q^{48} - 169724 q^{49} - 5730 q^{51} - 36540 q^{52} - 54640 q^{53} + 94827 q^{54} - 54762 q^{56} - 45460 q^{57} - 1830 q^{58} + 25386 q^{59} + 1400 q^{61} + 159480 q^{62} + 176820 q^{63} + 473442 q^{64} - 14616 q^{66} - 12660 q^{67} + 122245 q^{68} + 25464 q^{69} + 338280 q^{71} - 29955 q^{72} + 122460 q^{73} + 129612 q^{74} - 1409 q^{76} - 70380 q^{77} - 298280 q^{78} + 102054 q^{79} - 331320 q^{81} + 42570 q^{82} + 290250 q^{83} + 386436 q^{84} - 155085 q^{86} + 154910 q^{87} - 13515 q^{88} + 266988 q^{89} + 108836 q^{91} - 276990 q^{92} - 75180 q^{93} + 15490 q^{94} + 992700 q^{96} + 209820 q^{97} - 1187510 q^{98} - 294534 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)