Properties

Label 1350.2.c
Level $1350$
Weight $2$
Character orbit 1350.c
Rep. character $\chi_{1350}(649,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $12$
Sturm bound $540$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1350.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(540\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1350, [\chi])\).

Total New Old
Modular forms 306 24 282
Cusp forms 234 24 210
Eisenstein series 72 0 72

Trace form

\( 24 q - 24 q^{4} + O(q^{10}) \) \( 24 q - 24 q^{4} + 24 q^{16} - 12 q^{19} + 24 q^{34} + 48 q^{49} - 12 q^{61} - 24 q^{64} + 12 q^{76} + 36 q^{79} + 96 q^{91} - 72 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1350.2.c.a 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-3q^{11}+\cdots\)
1350.2.c.b 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-3q^{11}+\cdots\)
1350.2.c.c 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-3q^{11}+\cdots\)
1350.2.c.d 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}-3q^{11}+\cdots\)
1350.2.c.e 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}-3q^{11}+\cdots\)
1350.2.c.f 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+2iq^{13}+\cdots\)
1350.2.c.g 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+2iq^{13}+\cdots\)
1350.2.c.h 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+3q^{11}+\cdots\)
1350.2.c.i 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+3q^{11}+\cdots\)
1350.2.c.j 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+3q^{11}+\cdots\)
1350.2.c.k 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+3q^{11}+\cdots\)
1350.2.c.l 1350.c 5.b $2$ $10.780$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+3q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)