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Properties

Label 1464.2.a
Level $1464$
Weight $2$
Character orbit 1464.a
Rep. character $\chi_{1464}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $13$
Sturm bound $496$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1464 = 2^{3} \cdot 3 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1464.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(496\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1464))\).

Total New Old
Modular forms 256 30 226
Cusp forms 241 30 211
Eisenstein series 15 0 15

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

\(2\)\(3\)\(61\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(12\)
Minus space\(-\)\(18\)

Trace form

\( 30 q - 4 q^{7} + 30 q^{9} + O(q^{10}) \) \( 30 q - 4 q^{7} + 30 q^{9} - 8 q^{11} - 4 q^{15} - 8 q^{19} - 4 q^{21} + 34 q^{25} - 12 q^{31} + 8 q^{33} - 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 12 q^{43} + 24 q^{47} + 58 q^{49} + 12 q^{51} - 8 q^{53} + 8 q^{55} - 8 q^{57} + 16 q^{59} - 6 q^{61} - 4 q^{63} + 12 q^{65} + 36 q^{67} - 16 q^{69} + 24 q^{71} - 12 q^{73} - 12 q^{77} + 4 q^{79} + 30 q^{81} + 8 q^{83} - 8 q^{85} + 12 q^{87} + 8 q^{89} - 8 q^{91} + 20 q^{93} + 16 q^{95} - 16 q^{97} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1464))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 61
1464.2.a.a 1464.a 1.a $1$ $11.690$ \(\Q\) None 1464.2.a.a \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
1464.2.a.b 1464.a 1.a $1$ $11.690$ \(\Q\) None 1464.2.a.b \(0\) \(-1\) \(-2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
1464.2.a.c 1464.a 1.a $1$ $11.690$ \(\Q\) None 1464.2.a.c \(0\) \(-1\) \(1\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}-5q^{13}+\cdots\)
1464.2.a.d 1464.a 1.a $1$ $11.690$ \(\Q\) None 1464.2.a.d \(0\) \(-1\) \(3\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}+2q^{7}+q^{9}-6q^{11}+\cdots\)
1464.2.a.e 1464.a 1.a $1$ $11.690$ \(\Q\) None 1464.2.a.e \(0\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1464.2.a.f 1464.a 1.a $1$ $11.690$ \(\Q\) None 1464.2.a.f \(0\) \(1\) \(1\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}-q^{13}+\cdots\)
1464.2.a.g 1464.a 1.a $2$ $11.690$ \(\Q(\sqrt{6}) \) None 1464.2.a.g \(0\) \(-2\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+2\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
1464.2.a.h 1464.a 1.a $2$ $11.690$ \(\Q(\sqrt{6}) \) None 1464.2.a.h \(0\) \(-2\) \(6\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}+(-1-\beta )q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots\)
1464.2.a.i 1464.a 1.a $3$ $11.690$ 3.3.961.1 None 1464.2.a.i \(0\) \(-3\) \(-2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots\)
1464.2.a.j 1464.a 1.a $4$ $11.690$ 4.4.7232.1 None 1464.2.a.j \(0\) \(-4\) \(2\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+\cdots\)
1464.2.a.k 1464.a 1.a $4$ $11.690$ 4.4.9248.1 None 1464.2.a.k \(0\) \(4\) \(-6\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-2-\beta _{2})q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1464.2.a.l 1464.a 1.a $4$ $11.690$ 4.4.15317.1 None 1464.2.a.l \(0\) \(4\) \(6\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(2+\beta _{2})q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
1464.2.a.m 1464.a 1.a $5$ $11.690$ 5.5.4383968.1 None 1464.2.a.m \(0\) \(5\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1464))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1464)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(122))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(244))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(366))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(488))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(732))\)\(^{\oplus 2}\)