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Properties

Label 325.6.m
Level $325$
Weight $6$
Character orbit 325.m
Rep. character $\chi_{325}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $208$
Sturm bound $210$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 360 216 144
Cusp forms 336 208 128
Eisenstein series 24 8 16

Trace form

\( 208 q - 1662 q^{4} - 6 q^{6} + 8646 q^{9} + O(q^{10}) \) \( 208 q - 1662 q^{4} - 6 q^{6} + 8646 q^{9} - 66 q^{11} + 1240 q^{14} - 28354 q^{16} + 2916 q^{19} - 25500 q^{24} - 17152 q^{26} + 3612 q^{29} + 183240 q^{36} - 1540 q^{39} - 16554 q^{41} - 20346 q^{46} - 278768 q^{49} - 130184 q^{51} - 79782 q^{54} - 20198 q^{56} - 65376 q^{59} + 40516 q^{61} + 958904 q^{64} + 146388 q^{66} - 138316 q^{69} + 199014 q^{71} + 55074 q^{74} + 42432 q^{76} + 113256 q^{79} - 841632 q^{81} + 670860 q^{84} - 38964 q^{89} - 631934 q^{91} + 258946 q^{94} + O(q^{100}) \)

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

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