Properties

Label 1450.2.b
Level $1450$
Weight $2$
Character orbit 1450.b
Rep. character $\chi_{1450}(349,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $12$
Sturm bound $450$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1450.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(450\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1450, [\chi])\).

Total New Old
Modular forms 238 42 196
Cusp forms 214 42 172
Eisenstein series 24 0 24

Trace form

\( 42 q - 42 q^{4} - 34 q^{9} + O(q^{10}) \) \( 42 q - 42 q^{4} - 34 q^{9} - 4 q^{11} + 42 q^{16} + 4 q^{19} - 16 q^{21} - 4 q^{26} + 6 q^{29} - 32 q^{31} + 34 q^{36} + 32 q^{39} + 24 q^{41} + 4 q^{44} - 16 q^{46} - 34 q^{49} + 28 q^{51} + 24 q^{54} - 12 q^{59} + 20 q^{61} - 42 q^{64} - 60 q^{66} + 56 q^{69} - 56 q^{71} - 24 q^{74} - 4 q^{76} - 56 q^{79} - 6 q^{81} + 16 q^{84} - 4 q^{86} + 88 q^{89} + 32 q^{91} - 24 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1450, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1450.2.b.a 1450.b 5.b $2$ $11.578$ \(\Q(\sqrt{-1}) \) None 1450.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+2iq^{7}+\cdots\)
1450.2.b.b 1450.b 5.b $2$ $11.578$ \(\Q(\sqrt{-1}) \) None 58.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-2iq^{7}+\cdots\)
1450.2.b.c 1450.b 5.b $2$ $11.578$ \(\Q(\sqrt{-1}) \) None 1450.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{8}+3q^{9}-2q^{11}+\cdots\)
1450.2.b.d 1450.b 5.b $2$ $11.578$ \(\Q(\sqrt{-1}) \) None 290.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-2iq^{7}+iq^{8}+3q^{9}+\cdots\)
1450.2.b.e 1450.b 5.b $2$ $11.578$ \(\Q(\sqrt{-1}) \) None 1450.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
1450.2.b.f 1450.b 5.b $2$ $11.578$ \(\Q(\sqrt{-1}) \) None 58.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+3iq^{3}-q^{4}+3q^{6}-2iq^{7}+\cdots\)
1450.2.b.g 1450.b 5.b $4$ $11.578$ \(\Q(i, \sqrt{13})\) None 290.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{3})q^{6}+\cdots\)
1450.2.b.h 1450.b 5.b $4$ $11.578$ \(\Q(i, \sqrt{13})\) None 290.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{3})q^{6}+\cdots\)
1450.2.b.i 1450.b 5.b $4$ $11.578$ \(\Q(i, \sqrt{6})\) None 1450.2.a.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{3}q^{6}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
1450.2.b.j 1450.b 5.b $6$ $11.578$ 6.0.14077504.1 None 290.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{4}q^{3}-q^{4}-\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots\)
1450.2.b.k 1450.b 5.b $6$ $11.578$ 6.0.399424.1 None 1450.2.a.q \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{3}q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1450.2.b.l 1450.b 5.b $6$ $11.578$ 6.0.24681024.1 None 290.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+(1-\beta _{3}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1450, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)