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Properties

Label 315.10.i
Level $315$
Weight $10$
Character orbit 315.i
Rep. character $\chi_{315}(106,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $432$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
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 872 432 440
Cusp forms 856 432 424
Eisenstein series 16 0 16

Trace form

\( 432 q + 64 q^{2} + 292 q^{3} - 55296 q^{4} - 10460 q^{6} - 61992 q^{8} - 84916 q^{9} + O(q^{10}) \) \( 432 q + 64 q^{2} + 292 q^{3} - 55296 q^{4} - 10460 q^{6} - 61992 q^{8} - 84916 q^{9} + 116112 q^{11} - 853176 q^{12} + 132500 q^{15} - 14155776 q^{16} + 1453272 q^{17} - 1922828 q^{18} - 1575720 q^{19} + 19208 q^{21} + 2113344 q^{22} + 6716184 q^{23} + 3047824 q^{24} - 84375000 q^{25} + 30727568 q^{26} - 30526208 q^{27} + 2821696 q^{29} + 12580000 q^{30} + 20064256 q^{32} - 38240684 q^{33} - 7595532 q^{34} - 24010000 q^{35} - 49798964 q^{36} - 31684672 q^{38} + 135110676 q^{39} - 29092500 q^{40} + 40797828 q^{41} - 3141612 q^{43} - 483415872 q^{44} - 33820000 q^{45} - 20937096 q^{46} + 153226032 q^{47} + 251973736 q^{48} - 1245197016 q^{49} + 25000000 q^{50} + 191134864 q^{51} - 214046388 q^{52} - 416493680 q^{53} + 90468080 q^{54} + 1253265012 q^{57} + 427576644 q^{58} + 336492708 q^{59} + 135680000 q^{60} - 307001592 q^{62} - 79559536 q^{63} + 5972898096 q^{64} + 308690000 q^{65} + 1884657452 q^{66} + 457995924 q^{67} - 348774980 q^{68} - 906644040 q^{69} + 45623504 q^{71} - 3414216868 q^{72} + 1014053256 q^{73} + 516497596 q^{74} + 114062500 q^{75} + 771709788 q^{76} + 562448656 q^{77} + 3797143680 q^{78} - 204676524 q^{79} - 2140780000 q^{80} - 388973012 q^{81} + 1565026488 q^{82} + 3101651104 q^{83} - 1437344244 q^{84} + 255015000 q^{85} - 364899336 q^{86} + 5578186872 q^{87} + 1623048192 q^{88} + 307045120 q^{89} - 691520000 q^{90} - 859346712 q^{91} + 2021062616 q^{92} + 576622752 q^{93} - 3583917900 q^{94} + 2655690000 q^{95} - 4780095052 q^{96} - 295426116 q^{97} - 737894528 q^{98} + 944973280 q^{99} + O(q^{100}) \)

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

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)