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Properties

Label 325.6.p
Level $325$
Weight $6$
Character orbit 325.p
Rep. character $\chi_{325}(64,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $688$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.p (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 704 704 0
Cusp forms 688 688 0
Eisenstein series 16 16 0

Trace form

\( 688 q - 10 q^{3} - 2694 q^{4} + 13278 q^{9} + O(q^{10}) \) \( 688 q - 10 q^{3} - 2694 q^{4} + 13278 q^{9} - 524 q^{10} - 10 q^{12} - 5 q^{13} - 1766 q^{14} - 44666 q^{16} - 10 q^{17} - 1460 q^{22} + 4600 q^{23} - 16178 q^{25} - 11210 q^{26} - 10 q^{27} - 15740 q^{29} + 7124 q^{30} - 39860 q^{35} + 194734 q^{36} - 10 q^{38} + 9449 q^{39} + 4642 q^{40} - 77770 q^{42} + 281240 q^{48} + 1459792 q^{49} + 121108 q^{51} + 64960 q^{52} + 156460 q^{53} - 15264 q^{55} - 156084 q^{56} + 200966 q^{61} + 72280 q^{62} - 704630 q^{64} + 5082 q^{65} - 45706 q^{66} - 4152 q^{69} + 320960 q^{74} + 185168 q^{75} - 130400 q^{77} + 321345 q^{78} - 110662 q^{79} - 380086 q^{81} - 1141280 q^{87} + 923710 q^{88} + 635204 q^{90} + 41308 q^{91} - 399580 q^{92} + 42666 q^{94} - 183008 q^{95} + O(q^{100}) \)

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.