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Properties

Label 315.10.cb
Level $315$
Weight $10$
Character orbit 315.cb
Rep. character $\chi_{315}(13,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1712$
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.cb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1744 1744 0
Cusp forms 1712 1712 0
Eisenstein series 32 32 0

Trace form

\( 1712 q - 4 q^{2} - 2 q^{7} - 4112 q^{8} + O(q^{10}) \) \( 1712 q - 4 q^{2} - 2 q^{7} - 4112 q^{8} + 30816 q^{11} - 241760 q^{15} + 54525944 q^{16} - 278408 q^{18} + 630624 q^{21} + 4092 q^{22} - 2811852 q^{23} - 4 q^{25} - 1050632 q^{28} + 43987264 q^{30} - 15209712 q^{32} + 1089712 q^{35} - 104181776 q^{36} - 16 q^{37} + 42969218 q^{42} - 4 q^{43} - 51432224 q^{46} - 169595356 q^{50} - 120043624 q^{51} + 770396464 q^{53} - 31641280 q^{56} + 279508328 q^{57} + 205942396 q^{58} - 194778640 q^{60} - 145573446 q^{63} - 442301740 q^{65} - 4 q^{67} + 7812498 q^{70} - 765444160 q^{71} + 1497030340 q^{72} - 503474614 q^{77} + 1420578196 q^{78} - 1173092488 q^{81} - 4 q^{85} + 3384989264 q^{86} - 538966020 q^{88} - 16 q^{91} - 2161598468 q^{92} - 1567710212 q^{93} - 2259927320 q^{95} + 2733457680 q^{98} + O(q^{100}) \)

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.