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Properties

Label 675.2.q
Level $675$
Weight $2$
Character orbit 675.q
Rep. character $\chi_{675}(143,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $64$
Newform subspaces $3$
Sturm bound $180$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.q (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(180\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).

Total New Old
Modular forms 432 80 352
Cusp forms 288 64 224
Eisenstein series 144 16 128

Trace form

\( 64 q - 6 q^{2} + 2 q^{7} + O(q^{10}) \) \( 64 q - 6 q^{2} + 2 q^{7} + 36 q^{11} + 2 q^{13} + 16 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} - 12 q^{41} + 2 q^{43} - 112 q^{46} - 12 q^{47} + 14 q^{52} + 108 q^{56} + 6 q^{58} - 28 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} - 12 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} - 240 q^{86} - 18 q^{88} + 32 q^{91} - 60 q^{92} - 28 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
675.2.q.a 675.q 45.l $16$ $5.390$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{12}]$ \(q-\beta _{5}q^{2}+(\beta _{5}+\beta _{8}+\beta _{15})q^{4}+(\beta _{5}+\cdots)q^{7}+\cdots\)
675.2.q.b 675.q 45.l $16$ $5.390$ 16.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{11}q^{2}+(-\beta _{7}-\beta _{9})q^{4}+(-2\beta _{6}+\cdots)q^{7}+\cdots\)
675.2.q.c 675.q 45.l $32$ $5.390$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)