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Properties

Label 325.6.s
Level $325$
Weight $6$
Character orbit 325.s
Rep. character $\chi_{325}(32,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $412$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.s (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

\( 412 q - 6 q^{2} + 2 q^{3} - 3232 q^{4} - 8 q^{6} + 6 q^{7} + 648 q^{8} + 1320 q^{9} + O(q^{10}) \) \( 412 q - 6 q^{2} + 2 q^{3} - 3232 q^{4} - 8 q^{6} + 6 q^{7} + 648 q^{8} + 1320 q^{9} - 728 q^{11} + 1456 q^{12} - 2222 q^{13} - 49668 q^{16} - 2650 q^{17} + 5600 q^{19} + 1772 q^{21} + 3084 q^{22} + 7122 q^{23} + 14344 q^{24} + 1752 q^{26} - 9124 q^{27} - 186 q^{28} + 112 q^{31} + 376 q^{32} + 17458 q^{33} + 22728 q^{34} - 84492 q^{36} - 60702 q^{37} - 128 q^{38} - 38360 q^{39} - 28938 q^{41} + 15536 q^{42} + 12342 q^{43} + 179248 q^{44} + 107672 q^{46} - 146168 q^{48} + 362622 q^{49} + 166534 q^{52} + 14250 q^{53} + 67512 q^{54} - 241164 q^{56} - 232068 q^{57} + 71310 q^{58} - 164160 q^{59} - 28284 q^{61} + 137440 q^{62} + 120512 q^{63} + 1458432 q^{64} + 338544 q^{66} + 72058 q^{67} + 320192 q^{68} - 51360 q^{69} - 60728 q^{71} - 183354 q^{72} - 383792 q^{73} + 515880 q^{74} - 255592 q^{76} + 55652 q^{77} - 345952 q^{78} + 1457090 q^{81} + 583278 q^{82} - 1310392 q^{84} - 803488 q^{86} + 427858 q^{87} + 1091870 q^{88} + 161490 q^{89} + 701732 q^{91} - 746232 q^{92} - 100848 q^{93} - 104256 q^{94} + 1215752 q^{96} - 567178 q^{97} + 1033706 q^{98} + 780092 q^{99} + O(q^{100}) \)

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

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