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Properties

Label 315.5.o
Level $315$
Weight $5$
Character orbit 315.o
Rep. character $\chi_{315}(127,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 315.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(315, [\chi])\).

Total New Old
Modular forms 400 120 280
Cusp forms 368 120 248
Eisenstein series 32 0 32

Trace form

\( 120 q - 48 q^{5} + O(q^{10}) \) \( 120 q - 48 q^{5} + 496 q^{10} - 156 q^{11} - 640 q^{13} - 7736 q^{16} + 1320 q^{17} + 948 q^{20} - 2180 q^{22} - 1560 q^{23} - 2852 q^{25} - 6048 q^{26} + 2112 q^{31} + 5400 q^{32} + 1900 q^{37} - 4920 q^{38} - 5860 q^{40} - 624 q^{41} + 11860 q^{43} + 5584 q^{46} + 17580 q^{47} + 3888 q^{50} - 28560 q^{52} - 9360 q^{53} - 15940 q^{55} - 10584 q^{56} - 8380 q^{58} + 15544 q^{61} + 24720 q^{62} - 5220 q^{65} + 10860 q^{67} + 4440 q^{68} + 6272 q^{70} - 23760 q^{71} + 6940 q^{73} - 30968 q^{76} + 5880 q^{77} + 14148 q^{80} + 33320 q^{82} - 47280 q^{83} + 17856 q^{85} - 8952 q^{86} + 31080 q^{88} - 11172 q^{91} - 4080 q^{92} + 38412 q^{95} - 15120 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{5}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)