↑

Properties

Label 325.6.x
Level $325$
Weight $6$
Character orbit 325.x
Rep. character $\chi_{325}(7,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $412$
Sturm bound $210$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(210\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(325, [\chi])\).

Total New Old
Modular forms 724 428 296
Cusp forms 676 412 264
Eisenstein series 48 16 32

Trace form

\( 412 q + 6 q^{2} + 2 q^{3} + 3232 q^{4} - 8 q^{6} + 2 q^{7} - 1320 q^{9} + O(q^{10}) \) \( 412 q + 6 q^{2} + 2 q^{3} + 3232 q^{4} - 8 q^{6} + 2 q^{7} - 1320 q^{9} - 728 q^{11} - 1456 q^{12} - 1856 q^{13} - 49668 q^{16} - 4064 q^{17} + 1100 q^{18} - 5600 q^{19} + 1772 q^{21} + 3084 q^{22} - 7110 q^{23} - 14344 q^{24} + 1752 q^{26} - 9124 q^{27} - 4158 q^{28} + 112 q^{31} + 32232 q^{32} + 4182 q^{33} - 22728 q^{34} - 84492 q^{36} + 2584 q^{37} + 128 q^{38} + 38360 q^{39} - 28938 q^{41} - 69400 q^{42} - 12330 q^{43} - 179248 q^{44} + 107672 q^{46} - 7160 q^{47} + 97636 q^{48} - 362622 q^{49} - 193010 q^{52} + 14250 q^{53} - 67512 q^{54} - 241164 q^{56} - 52510 q^{58} + 164160 q^{59} - 28284 q^{61} + 86924 q^{62} - 98604 q^{63} - 1458432 q^{64} + 338544 q^{66} + 271662 q^{67} - 2272 q^{68} + 51360 q^{69} - 60728 q^{71} - 31474 q^{72} - 515880 q^{74} - 255592 q^{76} - 55652 q^{77} - 15708 q^{78} + 1457090 q^{81} + 81414 q^{82} + 273712 q^{83} + 1310392 q^{84} - 803488 q^{86} - 462926 q^{87} + 284638 q^{88} - 161490 q^{89} + 701732 q^{91} - 746232 q^{92} + 260488 q^{93} + 104256 q^{94} + 1215752 q^{96} + 511494 q^{97} - 1220310 q^{98} - 780092 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(325, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(325, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(325, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)