Properties

Label 1872.4.t
Level $1872$
Weight $4$
Character orbit 1872.t
Rep. character $\chi_{1872}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $208$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.t (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1872, [\chi])\).

Total New Old
Modular forms 2064 212 1852
Cusp forms 1968 208 1760
Eisenstein series 96 4 92

Trace form

\( 208 q + 6 q^{5} + 19 q^{7} + O(q^{10}) \) \( 208 q + 6 q^{5} + 19 q^{7} - q^{11} - 25 q^{13} + 14 q^{17} - 179 q^{19} - 139 q^{23} + 5018 q^{25} + 72 q^{29} - 116 q^{31} + 294 q^{35} - 34 q^{37} + 238 q^{41} - 557 q^{43} + 740 q^{47} - 5035 q^{49} - 674 q^{53} + 170 q^{55} + 645 q^{59} + 138 q^{61} - 687 q^{65} + 343 q^{67} + 987 q^{71} - 590 q^{73} - 1154 q^{77} + 968 q^{79} + 1336 q^{83} - 109 q^{85} + 199 q^{89} - 489 q^{91} - 2904 q^{95} + 605 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 2}\)