Properties

Label 2352.2.a
Level $2352$
Weight $2$
Character orbit 2352.a
Rep. character $\chi_{2352}(1,\cdot)$
Character field $\Q$
Dimension $41$
Newform subspaces $33$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 33 \)
Sturm bound: \(896\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2352))\).

Total New Old
Modular forms 496 41 455
Cusp forms 401 41 360
Eisenstein series 95 0 95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(18\)
Minus space\(-\)\(23\)

Trace form

\( 41q - q^{3} - 2q^{5} + 41q^{9} + O(q^{10}) \) \( 41q - q^{3} - 2q^{5} + 41q^{9} + 4q^{11} - 2q^{13} - 2q^{15} + 2q^{17} - 12q^{19} - 8q^{23} + 47q^{25} - q^{27} - 10q^{29} + 4q^{33} - 10q^{37} - 6q^{39} + 10q^{41} - 2q^{45} + 24q^{47} + 2q^{51} - 2q^{53} - 4q^{57} + 28q^{59} + 14q^{61} + 20q^{65} + 32q^{67} + 8q^{69} + 32q^{71} + 10q^{73} - 15q^{75} - 12q^{79} + 41q^{81} - 20q^{83} + 12q^{85} + 18q^{87} + 10q^{89} + 8q^{93} - 32q^{95} - 14q^{97} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
2352.2.a.a \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-4q^{5}+q^{9}-2q^{11}+6q^{13}+\cdots\)
2352.2.a.b \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-4q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots\)
2352.2.a.c \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}+q^{9}-6q^{13}+2q^{15}+\cdots\)
2352.2.a.d \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
2352.2.a.e \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}+q^{9}+6q^{11}+3q^{13}+\cdots\)
2352.2.a.f \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{9}-5q^{11}+q^{15}+4q^{17}+\cdots\)
2352.2.a.g \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
2352.2.a.h \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{9}+4q^{13}+4q^{17}+4q^{19}+\cdots\)
2352.2.a.i \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
2352.2.a.j \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
2352.2.a.k \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{9}-2q^{11}+3q^{13}+\cdots\)
2352.2.a.l \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
2352.2.a.m \(1\) \(18.781\) \(\Q\) None \(0\) \(-1\) \(3\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+3q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
2352.2.a.n \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-3q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
2352.2.a.o \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}+q^{9}-2q^{11}-3q^{13}+\cdots\)
2352.2.a.p \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\)
2352.2.a.q \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
2352.2.a.r \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}-4q^{13}-4q^{17}-4q^{19}+\cdots\)
2352.2.a.s \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{9}+6q^{11}-2q^{13}-4q^{19}+\cdots\)
2352.2.a.t \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+q^{9}-5q^{11}+q^{15}-4q^{17}+\cdots\)
2352.2.a.u \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
2352.2.a.v \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
2352.2.a.w \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+q^{9}+2q^{11}-q^{13}+\cdots\)
2352.2.a.x \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{5}+q^{9}+6q^{11}-3q^{13}+\cdots\)
2352.2.a.y \(1\) \(18.781\) \(\Q\) None \(0\) \(1\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+4q^{5}+q^{9}+4q^{11}+4q^{13}+\cdots\)
2352.2.a.z \(2\) \(18.781\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
2352.2.a.ba \(2\) \(18.781\) \(\Q(\sqrt{57}) \) None \(0\) \(-2\) \(1\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
2352.2.a.bb \(2\) \(18.781\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(4\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+(2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
2352.2.a.bc \(2\) \(18.781\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(4\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+(2+\beta )q^{5}+q^{9}+2q^{11}+(4+\cdots)q^{13}+\cdots\)
2352.2.a.bd \(2\) \(18.781\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
2352.2.a.be \(2\) \(18.781\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-4\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}+(-2+\beta )q^{5}+q^{9}+2q^{11}+\cdots\)
2352.2.a.bf \(2\) \(18.781\) \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(3-\beta )q^{13}+\cdots\)
2352.2.a.bg \(2\) \(18.781\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+(2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2352))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2352)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 2}\)