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Properties

Label 2205.4.dl
Level $2205$
Weight $4$
Character orbit 2205.dl
Rep. character $\chi_{2205}(236,\cdot)$
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.dl (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

\( 8064 q - 2688 q^{4} - 28 q^{6} + 12 q^{7} - 182 q^{9} + O(q^{10}) \) \( 8064 q - 2688 q^{4} - 28 q^{6} + 12 q^{7} - 182 q^{9} + 770 q^{12} + 72 q^{13} + 132 q^{14} + 10752 q^{16} - 28 q^{18} - 450 q^{21} - 1764 q^{23} - 144 q^{24} - 33600 q^{25} + 240 q^{26} + 48 q^{27} - 192 q^{28} + 756 q^{29} + 280 q^{30} + 360 q^{31} + 744 q^{33} + 560 q^{36} - 2184 q^{37} - 3480 q^{38} - 840 q^{39} - 618 q^{41} - 6240 q^{42} + 168 q^{43} - 2310 q^{44} + 990 q^{45} - 3276 q^{46} - 396 q^{47} + 2640 q^{48} + 636 q^{49} + 980 q^{51} + 2688 q^{52} - 2184 q^{53} + 864 q^{54} + 3174 q^{56} - 560 q^{57} + 1500 q^{59} + 6370 q^{60} + 9294 q^{61} + 664 q^{63} + 86016 q^{64} - 1968 q^{66} + 588 q^{67} + 9420 q^{68} + 10920 q^{69} - 180 q^{70} + 252 q^{72} - 5616 q^{77} - 14336 q^{78} - 420 q^{79} - 2814 q^{81} - 3660 q^{83} - 34928 q^{84} - 2636 q^{87} - 2226 q^{89} - 3510 q^{90} - 900 q^{91} - 43848 q^{92} - 2016 q^{93} - 8342 q^{96} + 1584 q^{97} - 11286 q^{98} - 11788 q^{99} + O(q^{100}) \)

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

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