Properties

Label 270.4.c
Level $270$
Weight $4$
Character orbit 270.c
Rep. character $\chi_{270}(109,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $5$
Sturm bound $216$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 270.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(216\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(270, [\chi])\).

Total New Old
Modular forms 174 24 150
Cusp forms 150 24 126
Eisenstein series 24 0 24

Trace form

\( 24 q - 96 q^{4} + O(q^{10}) \) \( 24 q - 96 q^{4} - 36 q^{10} + 384 q^{16} + 192 q^{19} + 222 q^{25} - 240 q^{31} - 984 q^{34} + 144 q^{40} - 360 q^{46} + 372 q^{49} - 1770 q^{55} + 1968 q^{61} - 1536 q^{64} + 876 q^{70} - 768 q^{76} - 1836 q^{79} + 2280 q^{85} + 6216 q^{91} - 3048 q^{94} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(270, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
270.4.c.a 270.c 5.b $2$ $15.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2iq^{2}-4q^{4}+(-10-5i)q^{5}+14iq^{7}+\cdots\)
270.4.c.b 270.c 5.b $2$ $15.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-4q^{4}+(10+5i)q^{5}+14iq^{7}+\cdots\)
270.4.c.c 270.c 5.b $6$ $15.931$ 6.0.\(\cdots\).1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{2}q^{2}-4q^{4}+\beta _{1}q^{5}+(\beta _{1}-7\beta _{2}+\cdots)q^{7}+\cdots\)
270.4.c.d 270.c 5.b $6$ $15.931$ 6.0.\(\cdots\).1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{2}q^{2}-4q^{4}-\beta _{1}q^{5}+(\beta _{1}-7\beta _{2}+\cdots)q^{7}+\cdots\)
270.4.c.e 270.c 5.b $8$ $15.931$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{1}q^{2}-4q^{4}+\beta _{3}q^{5}-\beta _{5}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(270, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(270, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)