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Properties

Label 2070.4.u
Level $2070$
Weight $4$
Character orbit 2070.u
Rep. character $\chi_{2070}(271,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $1200$
Sturm bound $1728$

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Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2070.u (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(1728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2070, [\chi])\).

Total New Old
Modular forms 13120 1200 11920
Cusp forms 12800 1200 11600
Eisenstein series 320 0 320

Trace form

\( 1200 q - 480 q^{4} + 10 q^{5} + O(q^{10}) \) \( 1200 q - 480 q^{4} + 10 q^{5} - 20 q^{10} - 108 q^{11} - 32 q^{13} - 80 q^{14} - 1920 q^{16} - 280 q^{17} + 428 q^{19} + 40 q^{20} + 880 q^{22} + 204 q^{23} - 3000 q^{25} + 352 q^{26} - 380 q^{29} - 1632 q^{31} + 624 q^{34} - 1210 q^{35} + 540 q^{37} + 392 q^{38} - 80 q^{40} + 564 q^{41} - 2980 q^{43} - 432 q^{44} + 72 q^{46} + 216 q^{47} - 3494 q^{49} - 128 q^{52} + 1120 q^{53} + 2100 q^{55} + 1616 q^{56} + 4480 q^{58} + 1822 q^{59} - 524 q^{61} - 2504 q^{62} - 7680 q^{64} + 340 q^{65} - 4284 q^{67} - 5696 q^{68} + 360 q^{70} - 1224 q^{71} - 3064 q^{73} - 3688 q^{74} - 48 q^{76} - 3424 q^{77} + 244 q^{79} + 160 q^{80} + 7920 q^{82} + 17848 q^{83} + 560 q^{85} + 6524 q^{86} - 352 q^{88} + 2828 q^{89} - 3896 q^{91} + 816 q^{92} - 384 q^{94} - 3200 q^{95} - 2276 q^{97} - 5120 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2070, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(2070, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)