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Properties

Label 2352.3.cj
Level $2352$
Weight $3$
Character orbit 2352.cj
Rep. character $\chi_{2352}(113,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1332$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2352.cj (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2352, [\chi])\).

Total New Old
Modular forms 5448 1356 4092
Cusp forms 5304 1332 3972
Eisenstein series 144 24 120

Trace form

\( 1332 q + 5 q^{3} + 4 q^{7} - 5 q^{9} + O(q^{10}) \) \( 1332 q + 5 q^{3} + 4 q^{7} - 5 q^{9} - 10 q^{13} + 23 q^{15} + 56 q^{19} + 11 q^{21} + 1044 q^{25} + 5 q^{27} - 88 q^{31} - 23 q^{33} - 10 q^{37} - 13 q^{39} + 234 q^{43} - 135 q^{45} + 36 q^{49} - 57 q^{51} + 110 q^{55} - 50 q^{57} - 10 q^{61} + 109 q^{63} - 40 q^{67} + 9 q^{69} - 202 q^{73} + 757 q^{75} - 88 q^{79} + 35 q^{81} - 110 q^{85} + 167 q^{87} - 486 q^{91} - 210 q^{93} + 104 q^{97} - 114 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)