Properties

Label 3150.2.g
Level $3150$
Weight $2$
Character orbit 3150.g
Rep. character $\chi_{3150}(2899,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $22$
Sturm bound $1440$
Trace bound $26$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(1440\)
Trace bound: \(26\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 768 44 724
Cusp forms 672 44 628
Eisenstein series 96 0 96

Trace form

\( 44 q - 44 q^{4} + O(q^{10}) \) \( 44 q - 44 q^{4} - 4 q^{11} - 4 q^{14} + 44 q^{16} - 16 q^{19} - 12 q^{26} + 16 q^{29} - 40 q^{31} + 28 q^{34} - 44 q^{41} + 4 q^{44} - 16 q^{46} - 44 q^{49} + 4 q^{56} + 20 q^{59} + 36 q^{61} - 44 q^{64} + 24 q^{71} + 16 q^{74} + 16 q^{76} - 56 q^{79} + 56 q^{86} - 36 q^{89} + 20 q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3150.2.g.a 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-6q^{11}+\cdots\)
3150.2.g.b 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-4q^{11}+\cdots\)
3150.2.g.c 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-4q^{11}+\cdots\)
3150.2.g.d 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-4q^{11}+\cdots\)
3150.2.g.e 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-4q^{11}+\cdots\)
3150.2.g.f 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-3q^{11}+\cdots\)
3150.2.g.g 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-2q^{11}+\cdots\)
3150.2.g.h 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-2q^{11}+\cdots\)
3150.2.g.i 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+2iq^{13}+\cdots\)
3150.2.g.j 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-4iq^{13}+\cdots\)
3150.2.g.k 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-iq^{13}+\cdots\)
3150.2.g.l 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-2iq^{13}+\cdots\)
3150.2.g.m 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+2iq^{13}+\cdots\)
3150.2.g.n 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-iq^{13}+\cdots\)
3150.2.g.o 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+2iq^{13}+\cdots\)
3150.2.g.p 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+2q^{11}+\cdots\)
3150.2.g.q 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+4q^{11}+\cdots\)
3150.2.g.r 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+4q^{11}+\cdots\)
3150.2.g.s 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+4q^{11}+\cdots\)
3150.2.g.t 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+4q^{11}+\cdots\)
3150.2.g.u 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+4q^{11}+\cdots\)
3150.2.g.v 3150.g 5.b $2$ $25.153$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+5q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)