Properties

Label 6300.2.k
Level $6300$
Weight $2$
Character orbit 6300.k
Rep. character $\chi_{6300}(6049,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $20$
Sturm bound $2880$
Trace bound $41$

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Defining parameters

Level: \( N \) \(=\) \( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6300.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(2880\)
Trace bound: \(41\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6300, [\chi])\).

Total New Old
Modular forms 1512 44 1468
Cusp forms 1368 44 1324
Eisenstein series 144 0 144

Trace form

\( 44 q + O(q^{10}) \) \( 44 q + 8 q^{11} + 8 q^{19} - 8 q^{29} - 4 q^{31} + 4 q^{41} - 44 q^{49} - 28 q^{59} - 36 q^{61} - 36 q^{71} + 40 q^{79} + 12 q^{89} - 16 q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(6300, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6300.2.k.a 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}-6q^{11}-4iq^{13}+6iq^{17}+\cdots\)
6300.2.k.b 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-4q^{11}+2iq^{17}+6q^{19}+\cdots\)
6300.2.k.c 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}-3q^{11}-iq^{13}-3iq^{17}+\cdots\)
6300.2.k.d 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}-3q^{11}-4iq^{13}-2q^{19}+\cdots\)
6300.2.k.e 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}-2q^{11}-4iq^{13}-6iq^{17}+\cdots\)
6300.2.k.f 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}-2q^{11}-4iq^{13}-2iq^{17}+\cdots\)
6300.2.k.g 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}-2q^{11}+6iq^{13}+4iq^{17}+\cdots\)
6300.2.k.h 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}-q^{11}+4iq^{13}+2iq^{17}+\cdots\)
6300.2.k.i 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}-4iq^{13}+6iq^{17}-2q^{19}+\cdots\)
6300.2.k.j 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+4iq^{13}+6iq^{17}-2q^{19}+\cdots\)
6300.2.k.k 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}+q^{11}+2iq^{13}-6q^{19}+iq^{23}+\cdots\)
6300.2.k.l 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+q^{11}-2iq^{13}+8iq^{17}+\cdots\)
6300.2.k.m 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+2q^{11}-4iq^{13}-2iq^{17}+\cdots\)
6300.2.k.n 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}+3q^{11}-4iq^{13}-6iq^{17}+\cdots\)
6300.2.k.o 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+4q^{11}-2iq^{17}+6q^{19}+\cdots\)
6300.2.k.p 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}+5q^{11}+3iq^{13}+iq^{17}+\cdots\)
6300.2.k.q 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}+5q^{11}-6iq^{13}+4iq^{17}+\cdots\)
6300.2.k.r 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+6q^{11}-2iq^{13}+4q^{19}+\cdots\)
6300.2.k.s 6300.k 5.b $4$ $50.306$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{7}+\zeta_{12}^{3}q^{11}+2\zeta_{12}q^{13}+\cdots\)
6300.2.k.t 6300.k 5.b $4$ $50.306$ \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{7}-\beta _{2}q^{11}+2\beta _{3}q^{17}+3\beta _{3}q^{23}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(6300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1260, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3150, [\chi])\)\(^{\oplus 2}\)