Properties

Label 2352.2.h
Level $2352$
Weight $2$
Character orbit 2352.h
Rep. character $\chi_{2352}(2255,\cdot)$
Character field $\Q$
Dimension $82$
Newform subspaces $16$
Sturm bound $896$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(896\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(47\)

Dimensions

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

Total New Old
Modular forms 496 82 414
Cusp forms 400 82 318
Eisenstein series 96 0 96

Trace form

\( 82q - 6q^{9} + O(q^{10}) \) \( 82q - 6q^{9} + 4q^{13} - 94q^{25} - 28q^{37} + 24q^{45} + 36q^{57} + 20q^{61} - 24q^{69} + 52q^{73} - 6q^{81} + 48q^{85} + 12q^{93} - 44q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2352.2.h.a \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-3q^{9}-7q^{13}+3\zeta_{6}q^{19}+\cdots\)
2352.2.h.b \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{3}-3q^{9}-5q^{13}+5\zeta_{6}q^{19}+\cdots\)
2352.2.h.c \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-3q^{9}+2q^{13}+2\zeta_{6}q^{19}+\cdots\)
2352.2.h.d \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-3q^{9}+5q^{13}-5\zeta_{6}q^{19}+\cdots\)
2352.2.h.e \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{3}-3q^{9}+7q^{13}-3\zeta_{6}q^{19}+\cdots\)
2352.2.h.f \(4\) \(18.781\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(0\) \(q+(-1+\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-1-2\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
2352.2.h.g \(4\) \(18.781\) \(\Q(\sqrt{-3}, \sqrt{-14})\) \(\Q(\sqrt{-21}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}-3q^{9}-\beta _{3}q^{11}+\cdots\)
2352.2.h.h \(4\) \(18.781\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(1-2\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
2352.2.h.i \(4\) \(18.781\) \(\Q(i, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{3}+(-1-2\beta _{3})q^{5}+\cdots\)
2352.2.h.j \(4\) \(18.781\) \(\Q(i, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(-1-2\beta _{3})q^{5}+(3+\beta _{3})q^{9}+\cdots\)
2352.2.h.k \(4\) \(18.781\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) \(q+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-1-2\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
2352.2.h.l \(8\) \(18.781\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{3}+\zeta_{24}^{4}q^{5}-\zeta_{24}^{5}q^{9}+\cdots\)
2352.2.h.m \(8\) \(18.781\) 8.0.8275904784.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{3}-\beta _{7}q^{5}+(-\beta _{4}-\beta _{7})q^{9}+\cdots\)
2352.2.h.n \(8\) \(18.781\) 8.0.8275904784.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-\beta _{7}q^{5}+(-\beta _{2}+\beta _{7})q^{9}+\cdots\)
2352.2.h.o \(8\) \(18.781\) 8.0.56070144.2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(1-\beta _{5}+\beta _{7})q^{9}+\cdots\)
2352.2.h.p \(16\) \(18.781\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{3}+\beta _{13}q^{5}-\beta _{3}q^{9}-\beta _{7}q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)