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Properties

Label 2352.2.bc
Level $2352$
Weight $2$
Character orbit 2352.bc
Rep. character $\chi_{2352}(1697,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $152$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 992 168 824
Cusp forms 800 152 648
Eisenstein series 192 16 176

Trace form

\( 152 q - 3 q^{3} + q^{9} + O(q^{10}) \) \( 152 q - 3 q^{3} + q^{9} + 14 q^{15} - 12 q^{19} - 54 q^{25} - 48 q^{31} + 3 q^{33} + 2 q^{37} - 22 q^{39} + 44 q^{43} + 15 q^{45} + 21 q^{51} + 30 q^{57} + 6 q^{61} - 32 q^{67} + 18 q^{73} + 66 q^{75} + 44 q^{79} - 11 q^{81} - 68 q^{85} + 60 q^{87} - 19 q^{93} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)