Properties

Label 2352.2.bl
Level $2352$
Weight $2$
Character orbit 2352.bl
Rep. character $\chi_{2352}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $20$
Sturm bound $896$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 20 \)
Sturm bound: \(896\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\), \(19\), \(31\)

Dimensions

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

Total New Old
Modular forms 992 80 912
Cusp forms 800 80 720
Eisenstein series 192 0 192

Trace form

\( 80q - 40q^{9} + O(q^{10}) \) \( 80q - 40q^{9} + 28q^{25} - 36q^{33} - 4q^{37} + 24q^{53} + 8q^{57} + 72q^{61} + 24q^{65} - 12q^{73} - 40q^{81} - 144q^{85} + 52q^{93} + O(q^{100}) \)

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.bl.a \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-6\) \(0\) \(q+(-1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.bl.b \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(0\) \(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.bl.c \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-2-2\zeta_{6})q^{11}+\cdots\)
2352.2.bl.d \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(2+2\zeta_{6})q^{11}+\cdots\)
2352.2.bl.e \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(0\) \(q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.bl.f \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(6\) \(0\) \(q+(-1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.bl.g \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-6\) \(0\) \(q+(1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.bl.h \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(0\) \(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.bl.i \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-2-2\zeta_{6})q^{11}+\cdots\)
2352.2.bl.j \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(2+2\zeta_{6})q^{11}+\cdots\)
2352.2.bl.k \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(0\) \(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.bl.l \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(6\) \(0\) \(q+(1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.bl.m \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1-\beta _{1})q^{3}+\beta _{3}q^{5}+\beta _{1}q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
2352.2.bl.n \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta _{1})q^{3}+\beta _{3}q^{5}+\beta _{1}q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
2352.2.bl.o \(8\) \(18.781\) 8.0.339738624.1 None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{4}q^{3}+(\beta _{2}-\beta _{3}-\beta _{6})q^{5}+(-1+\cdots)q^{9}+\cdots\)
2352.2.bl.p \(8\) \(18.781\) 8.0.339738624.1 None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{4})q^{3}+(-\beta _{3}-\beta _{7})q^{5}+\beta _{4}q^{9}+\cdots\)
2352.2.bl.q \(8\) \(18.781\) 8.0.339738624.1 None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{4}q^{3}+(-\beta _{2}+\beta _{3}+\beta _{6})q^{5}+(-1+\cdots)q^{9}+\cdots\)
2352.2.bl.r \(8\) \(18.781\) 8.0.339738624.1 None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{4}q^{3}+(-\beta _{2}+\beta _{3}+\beta _{6})q^{5}+(-1+\cdots)q^{9}+\cdots\)
2352.2.bl.s \(8\) \(18.781\) 8.0.339738624.1 None \(0\) \(4\) \(0\) \(0\) \(q+(1+\beta _{4})q^{3}+(-\beta _{3}-\beta _{7})q^{5}+\beta _{4}q^{9}+\cdots\)
2352.2.bl.t \(8\) \(18.781\) 8.0.339738624.1 None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{4}q^{3}+(\beta _{2}-\beta _{3}-\beta _{6})q^{5}+(-1+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)