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Properties

Label 2205.4.dw
Level $2205$
Weight $4$
Character orbit 2205.dw
Rep. character $\chi_{2205}(101,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $8064$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.dw (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2205, [\chi])\).

Total New Old
Modular forms 12144 8064 4080
Cusp forms 12048 8064 3984
Eisenstein series 96 0 96

Trace form

\( 8064 q + 5376 q^{4} - 28 q^{6} + 12 q^{7} + 70 q^{9} + O(q^{10}) \) \( 8064 q + 5376 q^{4} - 28 q^{6} + 12 q^{7} + 70 q^{9} - 1210 q^{12} - 72 q^{13} + 1032 q^{14} - 21504 q^{16} - 154 q^{18} - 144 q^{21} - 252 q^{23} + 16800 q^{25} - 240 q^{26} - 132 q^{27} - 192 q^{28} - 126 q^{29} - 140 q^{30} + 560 q^{36} - 2184 q^{37} - 1740 q^{38} + 420 q^{39} + 618 q^{41} + 1788 q^{42} + 168 q^{43} + 2310 q^{44} + 990 q^{45} - 3276 q^{46} + 1980 q^{47} - 2640 q^{48} + 42 q^{49} - 1120 q^{51} - 4224 q^{52} + 2184 q^{53} - 2586 q^{54} - 384 q^{56} - 560 q^{57} + 3000 q^{59} - 2450 q^{60} - 5880 q^{61} - 3308 q^{63} + 86016 q^{64} + 12834 q^{66} - 1176 q^{67} + 4710 q^{68} + 10920 q^{69} + 360 q^{70} + 1050 q^{72} - 2520 q^{74} - 5616 q^{77} + 23884 q^{78} + 840 q^{79} + 12390 q^{81} + 3660 q^{83} - 18368 q^{84} - 4158 q^{86} + 1852 q^{87} + 2226 q^{89} + 3510 q^{90} - 900 q^{91} + 12012 q^{92} + 1008 q^{93} - 13622 q^{96} - 1584 q^{97} + 11286 q^{98} - 11788 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)