Properties

Label 4368.2.a
Level $4368$
Weight $2$
Character orbit 4368.a
Rep. character $\chi_{4368}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $45$
Sturm bound $1792$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4368.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 45 \)
Sturm bound: \(1792\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4368))\).

Total New Old
Modular forms 920 72 848
Cusp forms 873 72 801
Eisenstein series 47 0 47

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

\(2\)\(3\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(32\)
Minus space\(-\)\(40\)

Trace form

\( 72q - 4q^{7} + 72q^{9} + O(q^{10}) \) \( 72q - 4q^{7} + 72q^{9} - 8q^{11} - 8q^{15} - 16q^{19} - 8q^{23} + 72q^{25} + 16q^{29} - 16q^{31} + 16q^{37} - 8q^{39} - 24q^{43} + 72q^{49} - 16q^{51} + 16q^{53} - 16q^{55} + 32q^{61} - 4q^{63} + 16q^{67} + 32q^{69} + 40q^{71} - 16q^{75} + 16q^{77} - 24q^{79} + 72q^{81} + 48q^{83} + 16q^{85} + 12q^{91} - 16q^{93} + 24q^{95} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4368))\) 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 13
4368.2.a.a \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(-3\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-3q^{5}-q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4368.2.a.b \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
4368.2.a.c \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{5}+q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
4368.2.a.d \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
4368.2.a.e \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}-q^{13}+\cdots\)
4368.2.a.f \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}+2q^{11}-q^{13}-6q^{17}+\cdots\)
4368.2.a.g \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots\)
4368.2.a.h \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
4368.2.a.i \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4368.2.a.j \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
4368.2.a.k \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
4368.2.a.l \(1\) \(34.879\) \(\Q\) None \(0\) \(-1\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+3q^{5}-q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
4368.2.a.m \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(-3\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-3q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
4368.2.a.n \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(-3\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-3q^{5}-q^{7}+q^{9}+5q^{11}-q^{13}+\cdots\)
4368.2.a.o \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
4368.2.a.p \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
4368.2.a.q \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
4368.2.a.r \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
4368.2.a.s \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
4368.2.a.t \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{7}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots\)
4368.2.a.u \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}+4q^{17}+\cdots\)
4368.2.a.v \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{5}-q^{7}+q^{9}-5q^{11}+q^{13}+\cdots\)
4368.2.a.w \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+6q^{11}-q^{13}+\cdots\)
4368.2.a.x \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
4368.2.a.y \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(2\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+q^{7}+q^{9}+q^{13}+2q^{15}+\cdots\)
4368.2.a.z \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(3\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
4368.2.a.ba \(1\) \(34.879\) \(\Q\) None \(0\) \(1\) \(4\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}+4q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
4368.2.a.bb \(2\) \(34.879\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-3\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
4368.2.a.bc \(2\) \(34.879\) \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
4368.2.a.bd \(2\) \(34.879\) \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(1\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
4368.2.a.be \(2\) \(34.879\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(3\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4368.2.a.bf \(2\) \(34.879\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-3\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
4368.2.a.bg \(2\) \(34.879\) \(\Q(\sqrt{41}) \) None \(0\) \(2\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
4368.2.a.bh \(2\) \(34.879\) \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-\beta q^{5}-q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4368.2.a.bi \(2\) \(34.879\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-1\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-\beta q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4368.2.a.bj \(2\) \(34.879\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}-2q^{11}-q^{13}+(2+\cdots)q^{17}+\cdots\)
4368.2.a.bk \(2\) \(34.879\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(1\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4368.2.a.bl \(2\) \(34.879\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4368.2.a.bm \(3\) \(34.879\) 3.3.2089.1 None \(0\) \(-3\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
4368.2.a.bn \(3\) \(34.879\) 3.3.1373.1 None \(0\) \(-3\) \(1\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
4368.2.a.bo \(3\) \(34.879\) 3.3.961.1 None \(0\) \(-3\) \(2\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
4368.2.a.bp \(3\) \(34.879\) 3.3.316.1 None \(0\) \(-3\) \(3\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4368.2.a.bq \(3\) \(34.879\) 3.3.316.1 None \(0\) \(3\) \(-3\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1-\beta _{1})q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4368.2.a.br \(4\) \(34.879\) 4.4.17428.1 None \(0\) \(-4\) \(-3\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+(-1-\beta _{2})q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
4368.2.a.bs \(4\) \(34.879\) 4.4.138892.1 None \(0\) \(4\) \(2\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4368))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4368)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1092))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2184))\)\(^{\oplus 2}\)