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Properties

Label 315.4.bl
Level $315$
Weight $4$
Character orbit 315.bl
Rep. character $\chi_{315}(41,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 315.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

Total New Old
Modular forms 296 192 104
Cusp forms 280 192 88
Eisenstein series 16 0 16

Trace form

\( 192 q + 384 q^{4} - 12 q^{7} - 4 q^{9} + O(q^{10}) \) \( 192 q + 384 q^{4} - 12 q^{7} - 4 q^{9} + 12 q^{11} - 282 q^{14} - 20 q^{15} - 1536 q^{16} + 364 q^{18} + 24 q^{21} + 504 q^{23} - 2400 q^{25} - 384 q^{28} - 252 q^{29} - 280 q^{30} + 3216 q^{36} - 672 q^{37} + 636 q^{39} + 438 q^{42} + 336 q^{43} - 1008 q^{46} - 42 q^{49} + 1020 q^{51} - 810 q^{56} - 1632 q^{57} - 660 q^{60} - 856 q^{63} - 12288 q^{64} - 960 q^{65} + 1176 q^{67} + 180 q^{70} - 6580 q^{72} + 10500 q^{74} + 5616 q^{77} + 660 q^{78} - 372 q^{79} + 7148 q^{81} - 9114 q^{84} + 360 q^{85} + 10716 q^{86} - 1800 q^{91} + 24024 q^{92} + 336 q^{93} - 6968 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)