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Properties

Label 315.10.be
Level $315$
Weight $10$
Character orbit 315.be
Rep. character $\chi_{315}(236,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $576$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 315.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(315, [\chi])\).

Total New Old
Modular forms 872 576 296
Cusp forms 856 576 280
Eisenstein series 16 0 16

Trace form

\( 576 q + 73728 q^{4} - 684 q^{7} - 17746 q^{9} + O(q^{10}) \) \( 576 q + 73728 q^{4} - 684 q^{7} - 17746 q^{9} - 194616 q^{13} + 191136 q^{14} - 132500 q^{15} - 18874368 q^{16} + 1660204 q^{18} + 553590 q^{21} + 5234688 q^{24} + 225000000 q^{25} - 11022720 q^{26} + 2113812 q^{27} + 700416 q^{28} + 8725122 q^{29} + 4760000 q^{30} - 23426280 q^{31} - 31592472 q^{33} + 24202824 q^{36} + 6476904 q^{37} + 154348440 q^{38} + 31014552 q^{39} - 3347706 q^{41} - 124940736 q^{42} - 32070024 q^{43} + 70411206 q^{44} - 31061250 q^{45} + 6429024 q^{46} + 116058492 q^{47} + 84986880 q^{48} - 53538372 q^{49} - 201089604 q^{51} - 311011656 q^{53} + 386455752 q^{54} - 644453862 q^{56} - 265550064 q^{57} - 72955500 q^{59} - 82893750 q^{60} - 525203082 q^{61} - 119540392 q^{63} - 9663676416 q^{64} - 69240000 q^{65} - 581971200 q^{66} - 278498556 q^{67} + 2027249940 q^{68} + 156060000 q^{70} - 1296773128 q^{72} + 1498681872 q^{77} + 421489704 q^{78} - 83541384 q^{79} + 773480438 q^{81} + 3717875580 q^{83} - 6031617804 q^{84} + 255015000 q^{85} - 204061476 q^{87} + 2706876102 q^{89} + 2708403750 q^{90} - 1754700300 q^{91} - 3677250444 q^{92} + 123013536 q^{93} + 10901789862 q^{96} - 1356263568 q^{97} + 3167872038 q^{98} + 8901336316 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)