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Properties

Label 2028.4.bg
Level $2028$
Weight $4$
Character orbit 2028.bg
Rep. character $\chi_{2028}(61,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $2208$
Sturm bound $1456$

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Defining parameters

Level: \( N \) \(=\) \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2028.bg (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(1456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2028, [\chi])\).

Total New Old
Modular forms 26352 2208 24144
Cusp forms 26064 2208 23856
Eisenstein series 288 0 288

Trace form

\( 2208 q - 20 q^{5} - 4 q^{7} + 828 q^{9} + O(q^{10}) \) \( 2208 q - 20 q^{5} - 4 q^{7} + 828 q^{9} - 8 q^{11} - 106 q^{13} + 12 q^{15} + 18 q^{17} + 64 q^{19} - 156 q^{21} - 128 q^{23} - 4804 q^{25} + 6 q^{29} - 996 q^{31} - 96 q^{33} + 464 q^{35} - 290 q^{37} + 180 q^{39} + 886 q^{41} + 90 q^{45} - 896 q^{47} + 4054 q^{49} - 288 q^{51} - 3642 q^{53} - 4392 q^{55} + 168 q^{57} - 1336 q^{59} + 2008 q^{61} - 36 q^{63} + 2146 q^{65} - 2220 q^{67} + 240 q^{69} - 10648 q^{71} - 3416 q^{73} - 312 q^{75} - 2968 q^{77} - 1552 q^{79} + 7452 q^{81} + 3360 q^{83} + 5680 q^{85} + 3660 q^{87} - 1028 q^{89} - 440 q^{91} - 2142 q^{93} + 5192 q^{95} + 7098 q^{97} + 144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2028, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2028, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2028, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)