Properties

Label 1824.2.a
Level $1824$
Weight $2$
Character orbit 1824.a
Rep. character $\chi_{1824}(1,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $22$
Sturm bound $640$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1824.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(640\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1824))\).

Total New Old
Modular forms 336 36 300
Cusp forms 305 36 269
Eisenstein series 31 0 31

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

\(2\)\(3\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(14\)
Minus space\(-\)\(22\)

Trace form

\( 36q - 8q^{5} + 36q^{9} + O(q^{10}) \) \( 36q - 8q^{5} + 36q^{9} - 8q^{13} + 24q^{17} + 44q^{25} - 8q^{29} - 16q^{33} - 8q^{37} + 24q^{41} - 8q^{45} + 20q^{49} - 8q^{53} - 8q^{61} + 48q^{65} + 8q^{73} + 48q^{77} + 36q^{81} + 32q^{85} + 24q^{89} + 72q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1824))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 19
1824.2.a.a \(1\) \(14.565\) \(\Q\) None \(0\) \(-1\) \(-2\) \(4\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
1824.2.a.b \(1\) \(14.565\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+3q^{11}+q^{15}+\cdots\)
1824.2.a.c \(1\) \(14.565\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots\)
1824.2.a.d \(1\) \(14.565\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+q^{9}-2q^{17}-q^{19}-6q^{23}+\cdots\)
1824.2.a.e \(1\) \(14.565\) \(\Q\) None \(0\) \(-1\) \(2\) \(-4\) \(-\) \(+\) \(+\) \(q-q^{3}+2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots\)
1824.2.a.f \(1\) \(14.565\) \(\Q\) None \(0\) \(-1\) \(3\) \(-3\) \(+\) \(+\) \(+\) \(q-q^{3}+3q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
1824.2.a.g \(1\) \(14.565\) \(\Q\) None \(0\) \(1\) \(-2\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
1824.2.a.h \(1\) \(14.565\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(-\) \(q+q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+4q^{13}+\cdots\)
1824.2.a.i \(1\) \(14.565\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-q^{15}+\cdots\)
1824.2.a.j \(1\) \(14.565\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{9}-2q^{17}+q^{19}+6q^{23}+\cdots\)
1824.2.a.k \(1\) \(14.565\) \(\Q\) None \(0\) \(1\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots\)
1824.2.a.l \(1\) \(14.565\) \(\Q\) None \(0\) \(1\) \(3\) \(3\) \(-\) \(-\) \(-\) \(q+q^{3}+3q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
1824.2.a.m \(2\) \(14.565\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-3\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
1824.2.a.n \(2\) \(14.565\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-3\) \(1\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
1824.2.a.o \(2\) \(14.565\) \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(-1\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
1824.2.a.p \(2\) \(14.565\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-3\) \(-1\) \(+\) \(-\) \(-\) \(q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
1824.2.a.q \(2\) \(14.565\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-3\) \(1\) \(+\) \(-\) \(+\) \(q+q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
1824.2.a.r \(2\) \(14.565\) \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
1824.2.a.s \(3\) \(14.565\) 3.3.469.1 None \(0\) \(-3\) \(-3\) \(5\) \(-\) \(+\) \(+\) \(q-q^{3}+(-1+\beta _{1})q^{5}+(2-\beta _{2})q^{7}+\cdots\)
1824.2.a.t \(3\) \(14.565\) 3.3.229.1 None \(0\) \(-3\) \(5\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{3}+(2+\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
1824.2.a.u \(3\) \(14.565\) 3.3.469.1 None \(0\) \(3\) \(-3\) \(-5\) \(-\) \(-\) \(-\) \(q+q^{3}+(-1+\beta _{1})q^{5}+(-2+\beta _{2})q^{7}+\cdots\)
1824.2.a.v \(3\) \(14.565\) 3.3.229.1 None \(0\) \(3\) \(5\) \(1\) \(+\) \(-\) \(+\) \(q+q^{3}+(2+\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1824))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1824)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 2}\)