Properties

Label 1425.2.c
Level $1425$
Weight $2$
Character orbit 1425.c
Rep. character $\chi_{1425}(799,\cdot)$
Character field $\Q$
Dimension $52$
Newform subspaces $16$
Sturm bound $400$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1425.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(400\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1425, [\chi])\).

Total New Old
Modular forms 212 52 160
Cusp forms 188 52 136
Eisenstein series 24 0 24

Trace form

\( 52 q - 48 q^{4} - 4 q^{6} - 52 q^{9} + O(q^{10}) \) \( 52 q - 48 q^{4} - 4 q^{6} - 52 q^{9} - 4 q^{11} - 32 q^{14} + 56 q^{16} + 8 q^{19} + 12 q^{24} + 8 q^{26} + 16 q^{29} + 24 q^{31} + 8 q^{34} + 48 q^{36} - 56 q^{41} + 8 q^{44} - 48 q^{46} - 40 q^{49} + 16 q^{51} + 4 q^{54} - 96 q^{59} - 28 q^{61} - 32 q^{64} - 16 q^{66} - 16 q^{69} + 96 q^{71} + 168 q^{74} - 20 q^{76} - 24 q^{79} + 52 q^{81} + 32 q^{84} - 8 q^{86} + 32 q^{89} - 32 q^{94} - 68 q^{96} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1425, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1425.2.c.a 1425.c 5.b $2$ $11.379$ \(\Q(\sqrt{-1}) \) None 57.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}-3iq^{7}+\cdots\)
1425.2.c.b 1425.c 5.b $2$ $11.379$ \(\Q(\sqrt{-1}) \) None 57.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+5iq^{7}+\cdots\)
1425.2.c.c 1425.c 5.b $2$ $11.379$ \(\Q(\sqrt{-1}) \) None 285.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+2iq^{7}+\cdots\)
1425.2.c.d 1425.c 5.b $2$ $11.379$ \(\Q(\sqrt{-1}) \) None 285.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}-2iq^{7}+\cdots\)
1425.2.c.e 1425.c 5.b $2$ $11.379$ \(\Q(\sqrt{-1}) \) None 1425.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}-4iq^{7}+\cdots\)
1425.2.c.f 1425.c 5.b $2$ $11.379$ \(\Q(\sqrt{-1}) \) None 285.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots\)
1425.2.c.g 1425.c 5.b $2$ $11.379$ \(\Q(\sqrt{-1}) \) None 57.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{8}+\cdots\)
1425.2.c.h 1425.c 5.b $2$ $11.379$ \(\Q(\sqrt{-1}) \) None 1425.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{8}+\cdots\)
1425.2.c.i 1425.c 5.b $4$ $11.379$ \(\Q(i, \sqrt{7})\) None 285.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{1}q^{3}-5q^{4}+\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1425.2.c.j 1425.c 5.b $4$ $11.379$ \(\Q(\zeta_{8})\) None 285.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1425.2.c.k 1425.c 5.b $4$ $11.379$ \(\Q(\zeta_{12})\) None 285.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{3}q^{6}+\cdots\)
1425.2.c.l 1425.c 5.b $4$ $11.379$ \(\Q(\zeta_{8})\) None 285.2.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1425.2.c.m 1425.c 5.b $4$ $11.379$ \(\Q(i, \sqrt{5})\) None 1425.2.a.n \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
1425.2.c.n 1425.c 5.b $4$ $11.379$ \(\Q(i, \sqrt{5})\) None 1425.2.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots\)
1425.2.c.o 1425.c 5.b $6$ $11.379$ 6.0.44836416.1 None 1425.2.a.t \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-2+\beta _{2})q^{4}-\beta _{4}q^{6}+\cdots\)
1425.2.c.p 1425.c 5.b $6$ $11.379$ 6.0.24681024.1 None 1425.2.a.u \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1425, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1425, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)