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Properties

Label 315.10.bj
Level $315$
Weight $10$
Character orbit 315.bj
Rep. character $\chi_{315}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 880 192 688
Cusp forms 848 192 656
Eisenstein series 32 0 32

Trace form

\( 192 q + 24576 q^{4} - 5016 q^{7} + O(q^{10}) \) \( 192 q + 24576 q^{4} - 5016 q^{7} - 6517896 q^{16} - 2948616 q^{19} + 7980480 q^{22} - 37500000 q^{25} + 2117064 q^{28} - 39043800 q^{31} - 31111080 q^{37} - 256404912 q^{43} + 30167640 q^{46} - 25817784 q^{49} - 718737768 q^{52} + 122975928 q^{58} - 130271904 q^{61} - 1900070400 q^{64} + 607752600 q^{67} + 553635000 q^{70} - 1552949496 q^{73} + 540717864 q^{79} - 5731024752 q^{82} + 5105941128 q^{88} + 4376495520 q^{91} - 16509595392 q^{94} + O(q^{100}) \)

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

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