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Properties

Label 315.10.p
Level $315$
Weight $10$
Character orbit 315.p
Rep. character $\chi_{315}(118,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $356$
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.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 880 364 516
Cusp forms 848 356 492
Eisenstein series 32 8 24

Trace form

\( 356 q + 4 q^{2} + 13566 q^{7} - 616 q^{8} + O(q^{10}) \) \( 356 q + 4 q^{2} + 13566 q^{7} - 616 q^{8} - 144664 q^{11} - 23618808 q^{16} + 4170492 q^{22} - 195388 q^{23} + 5731924 q^{25} - 10629088 q^{28} + 15946992 q^{32} - 26199522 q^{35} + 34038452 q^{37} - 52854436 q^{43} + 144523760 q^{46} - 133859468 q^{50} - 80010988 q^{53} + 180091384 q^{56} + 101250612 q^{58} + 861604340 q^{65} + 587780260 q^{67} + 765907860 q^{70} - 266898784 q^{71} + 1206381448 q^{77} + 173835228 q^{85} + 495750584 q^{86} - 5785867024 q^{88} + 4742903420 q^{91} - 2716254800 q^{92} - 3171191848 q^{95} + 485209668 q^{98} + O(q^{100}) \)

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

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