Properties

Label 1452.4.a
Level $1452$
Weight $4$
Character orbit 1452.a
Rep. character $\chi_{1452}(1,\cdot)$
Character field $\Q$
Dimension $55$
Newform subspaces $21$
Sturm bound $1056$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1452.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(1056\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1452))\).

Total New Old
Modular forms 828 55 773
Cusp forms 756 55 701
Eisenstein series 72 0 72

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

\(2\)\(3\)\(11\)FrickeDim
\(-\)\(+\)\(+\)$-$\(14\)
\(-\)\(+\)\(-\)$+$\(13\)
\(-\)\(-\)\(+\)$+$\(16\)
\(-\)\(-\)\(-\)$-$\(12\)
Plus space\(+\)\(29\)
Minus space\(-\)\(26\)

Trace form

\( 55 q + 3 q^{3} - 2 q^{5} - 12 q^{7} + 495 q^{9} + O(q^{10}) \) \( 55 q + 3 q^{3} - 2 q^{5} - 12 q^{7} + 495 q^{9} + 2 q^{13} + 54 q^{15} - 150 q^{17} - 64 q^{19} - 60 q^{21} - 240 q^{23} + 1073 q^{25} + 27 q^{27} + 46 q^{29} + 4 q^{31} + 672 q^{35} + 206 q^{37} - 54 q^{39} - 334 q^{41} + 112 q^{43} - 18 q^{45} - 224 q^{47} + 4147 q^{49} + 66 q^{51} + 406 q^{53} + 552 q^{57} + 940 q^{59} - 1382 q^{61} - 108 q^{63} - 172 q^{65} - 372 q^{67} + 96 q^{69} + 2680 q^{71} - 42 q^{73} - 75 q^{75} + 2556 q^{79} + 4455 q^{81} + 20 q^{83} - 2052 q^{85} + 150 q^{87} - 2182 q^{89} - 3400 q^{91} - 2448 q^{93} - 1864 q^{95} - 1530 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1452))\) 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 11
1452.4.a.a 1452.a 1.a $1$ $85.671$ \(\Q\) None 132.4.a.a \(0\) \(-3\) \(-12\) \(-14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-12q^{5}-14q^{7}+9q^{9}-56q^{13}+\cdots\)
1452.4.a.b 1452.a 1.a $1$ $85.671$ \(\Q\) None 132.4.a.b \(0\) \(-3\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+9q^{9}+88q^{13}+66q^{17}+\cdots\)
1452.4.a.c 1452.a 1.a $1$ $85.671$ \(\Q\) None 132.4.a.c \(0\) \(-3\) \(22\) \(20\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+22q^{5}+20q^{7}+9q^{9}-22q^{13}+\cdots\)
1452.4.a.d 1452.a 1.a $1$ $85.671$ \(\Q\) None 12.4.a.a \(0\) \(3\) \(-18\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-18q^{5}-8q^{7}+9q^{9}+10q^{13}+\cdots\)
1452.4.a.e 1452.a 1.a $1$ $85.671$ \(\Q\) None 1452.4.a.e \(0\) \(3\) \(-9\) \(-20\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-9q^{5}-20q^{7}+9q^{9}+37q^{13}+\cdots\)
1452.4.a.f 1452.a 1.a $1$ $85.671$ \(\Q\) None 1452.4.a.e \(0\) \(3\) \(-9\) \(20\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-9q^{5}+20q^{7}+9q^{9}-37q^{13}+\cdots\)
1452.4.a.g 1452.a 1.a $1$ $85.671$ \(\Q\) None 1452.4.a.g \(0\) \(3\) \(4\) \(-19\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+4q^{5}-19q^{7}+9q^{9}+54q^{13}+\cdots\)
1452.4.a.h 1452.a 1.a $1$ $85.671$ \(\Q\) None 1452.4.a.g \(0\) \(3\) \(4\) \(19\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+4q^{5}+19q^{7}+9q^{9}-54q^{13}+\cdots\)
1452.4.a.i 1452.a 1.a $1$ $85.671$ \(\Q\) None 132.4.a.d \(0\) \(3\) \(10\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+10q^{5}-8q^{7}+9q^{9}-18q^{13}+\cdots\)
1452.4.a.j 1452.a 1.a $2$ $85.671$ \(\Q(\sqrt{553}) \) None 1452.4.a.j \(0\) \(-6\) \(-5\) \(-21\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-2-\beta )q^{5}+(-11+\beta )q^{7}+\cdots\)
1452.4.a.k 1452.a 1.a $2$ $85.671$ \(\Q(\sqrt{553}) \) None 1452.4.a.j \(0\) \(-6\) \(-5\) \(21\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-2-\beta )q^{5}+(11-\beta )q^{7}+\cdots\)
1452.4.a.l 1452.a 1.a $2$ $85.671$ \(\Q(\sqrt{5}) \) None 132.4.i.a \(0\) \(-6\) \(1\) \(-22\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-5+11\beta )q^{5}+(-13+4\beta )q^{7}+\cdots\)
1452.4.a.m 1452.a 1.a $2$ $85.671$ \(\Q(\sqrt{5}) \) None 132.4.i.a \(0\) \(-6\) \(1\) \(22\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-5+11\beta )q^{5}+(13-4\beta )q^{7}+\cdots\)
1452.4.a.n 1452.a 1.a $2$ $85.671$ \(\Q(\sqrt{93}) \) None 1452.4.a.n \(0\) \(-6\) \(12\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+6q^{5}+\beta q^{7}+9q^{9}-2\beta q^{13}+\cdots\)
1452.4.a.o 1452.a 1.a $4$ $85.671$ 4.4.885025.1 None 132.4.i.b \(0\) \(-12\) \(-6\) \(-11\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(1+\beta _{1}+6\beta _{3})q^{5}+(-2-3\beta _{2}+\cdots)q^{7}+\cdots\)
1452.4.a.p 1452.a 1.a $4$ $85.671$ 4.4.885025.1 None 132.4.i.b \(0\) \(-12\) \(-6\) \(11\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(1+\beta _{1}+6\beta _{3})q^{5}+(2+3\beta _{2}+\cdots)q^{7}+\cdots\)
1452.4.a.q 1452.a 1.a $4$ $85.671$ 4.4.20959101.1 None 1452.4.a.q \(0\) \(12\) \(12\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(3+\beta _{3})q^{5}-\beta _{1}q^{7}+9q^{9}+\cdots\)
1452.4.a.r 1452.a 1.a $6$ $85.671$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 1452.4.a.r \(0\) \(-18\) \(-12\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-2-\beta _{4})q^{5}+(2\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
1452.4.a.s 1452.a 1.a $6$ $85.671$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 1452.4.a.s \(0\) \(18\) \(-12\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-2-\beta _{4})q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)
1452.4.a.t 1452.a 1.a $6$ $85.671$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 132.4.i.c \(0\) \(18\) \(13\) \(-23\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(2-\beta _{2})q^{5}+(-4+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
1452.4.a.u 1452.a 1.a $6$ $85.671$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 132.4.i.c \(0\) \(18\) \(13\) \(23\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(2-\beta _{2})q^{5}+(4-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1452))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1452)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 2}\)