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Properties

Label 325.6.q
Level $325$
Weight $6$
Character orbit 325.q
Rep. character $\chi_{325}(116,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $696$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.q (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(210\)

Dimensions

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

Total New Old
Modular forms 712 712 0
Cusp forms 696 696 0
Eisenstein series 16 16 0

Trace form

\( 696 q - 6 q^{3} + 2778 q^{4} - 14100 q^{9} + O(q^{10}) \) \( 696 q - 6 q^{3} + 2778 q^{4} - 14100 q^{9} - 692 q^{10} + 1630 q^{12} - 657 q^{13} - 1382 q^{14} - 40850 q^{16} + 822 q^{17} - 2056 q^{22} + 13304 q^{23} + 5256 q^{25} + 7394 q^{26} + 6018 q^{27} - 21640 q^{29} - 17600 q^{30} + 11284 q^{35} + 235942 q^{36} - 32870 q^{38} + 10421 q^{39} - 50354 q^{40} - 7394 q^{42} + 436 q^{43} + 117364 q^{48} - 1632696 q^{49} - 121140 q^{51} - 90260 q^{52} + 36238 q^{53} - 22088 q^{55} + 164264 q^{56} - 163078 q^{61} - 77828 q^{62} + 598282 q^{64} + 259783 q^{65} - 16514 q^{66} - 332812 q^{68} - 2208 q^{69} + 313104 q^{74} + 59736 q^{75} + 326544 q^{77} - 184293 q^{78} - 110662 q^{79} - 1680080 q^{81} + 859688 q^{82} - 601676 q^{87} + 206290 q^{88} - 224376 q^{90} - 41314 q^{91} + 117300 q^{92} + 42410 q^{94} + 765724 q^{95} + O(q^{100}) \)

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.