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Properties

Label 315.10.j
Level $315$
Weight $10$
Character orbit 315.j
Rep. character $\chi_{315}(46,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $240$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 880 240 640
Cusp forms 848 240 608
Eisenstein series 32 0 32

Trace form

\( 240 q + 34 q^{2} - 30890 q^{4} + 1250 q^{5} + 1140 q^{7} - 67932 q^{8} + O(q^{10}) \) \( 240 q + 34 q^{2} - 30890 q^{4} + 1250 q^{5} + 1140 q^{7} - 67932 q^{8} - 20000 q^{10} - 109734 q^{11} - 441856 q^{13} - 25882 q^{14} - 8276574 q^{16} + 609420 q^{17} + 1006502 q^{19} - 2825000 q^{20} + 2965664 q^{22} + 3432560 q^{23} - 46875000 q^{25} - 5493394 q^{26} + 2521562 q^{28} + 4462356 q^{29} - 9031840 q^{31} + 10360126 q^{32} - 69029192 q^{34} + 7591250 q^{35} + 41792404 q^{37} + 8525256 q^{38} - 15360000 q^{40} + 40581240 q^{41} + 4775216 q^{43} - 96230206 q^{44} + 25849954 q^{46} + 151776816 q^{47} - 86110330 q^{49} - 26562500 q^{50} + 174437316 q^{52} - 11557588 q^{53} + 68740000 q^{55} + 620709468 q^{56} - 212791290 q^{58} + 95453604 q^{59} - 465417750 q^{61} + 29977200 q^{62} + 4404608308 q^{64} + 108773750 q^{65} + 142855192 q^{67} + 1156434356 q^{68} - 795422500 q^{70} - 1276363792 q^{71} - 423304604 q^{73} - 836607962 q^{74} - 279007132 q^{76} + 3028751784 q^{77} + 237383720 q^{79} + 805120000 q^{80} - 2456701298 q^{82} - 876351216 q^{83} - 279520000 q^{85} - 2460256928 q^{86} + 654649928 q^{88} + 1448769182 q^{89} - 3398220028 q^{91} - 8402830052 q^{92} - 3587080178 q^{94} - 284437500 q^{95} - 6241284752 q^{97} + 4899763562 q^{98} + O(q^{100}) \)

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

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)