Properties

Label 2175.2.c
Level $2175$
Weight $2$
Character orbit 2175.c
Rep. character $\chi_{2175}(349,\cdot)$
Character field $\Q$
Dimension $84$
Newform subspaces $16$
Sturm bound $600$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2175.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(600\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2175, [\chi])\).

Total New Old
Modular forms 312 84 228
Cusp forms 288 84 204
Eisenstein series 24 0 24

Trace form

\( 84 q - 92 q^{4} + 8 q^{6} - 84 q^{9} + O(q^{10}) \) \( 84 q - 92 q^{4} + 8 q^{6} - 84 q^{9} + 8 q^{11} - 24 q^{14} + 124 q^{16} - 12 q^{19} - 12 q^{21} - 24 q^{24} + 8 q^{26} - 12 q^{31} - 48 q^{34} + 92 q^{36} + 20 q^{39} + 48 q^{41} - 48 q^{44} - 40 q^{46} - 136 q^{49} + 32 q^{51} - 8 q^{54} + 96 q^{56} - 72 q^{59} + 28 q^{61} - 148 q^{64} - 32 q^{66} - 32 q^{69} + 48 q^{71} + 40 q^{74} - 24 q^{76} - 24 q^{79} + 84 q^{81} + 40 q^{84} + 8 q^{86} - 72 q^{89} + 60 q^{91} + 24 q^{94} - 24 q^{96} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2175, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2175.2.c.a 2175.c 5.b $2$ $17.367$ \(\Q(\sqrt{-1}) \) None 435.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+4iq^{7}+\cdots\)
2175.2.c.b 2175.c 5.b $2$ $17.367$ \(\Q(\sqrt{-1}) \) None 435.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+4iq^{7}+\cdots\)
2175.2.c.c 2175.c 5.b $2$ $17.367$ \(\Q(\sqrt{-1}) \) None 2175.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2q^{4}-iq^{7}-q^{9}-2q^{11}+\cdots\)
2175.2.c.d 2175.c 5.b $2$ $17.367$ \(\Q(\sqrt{-1}) \) None 435.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2q^{4}+2iq^{7}-q^{9}+q^{11}+\cdots\)
2175.2.c.e 2175.c 5.b $2$ $17.367$ \(\Q(\sqrt{-1}) \) None 435.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{4}-2iq^{7}-q^{9}+3q^{11}+\cdots\)
2175.2.c.f 2175.c 5.b $4$ $17.367$ \(\Q(i, \sqrt{21})\) None 435.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-4+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
2175.2.c.g 2175.c 5.b $4$ $17.367$ \(\Q(i, \sqrt{5})\) None 435.2.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-3q^{4}-\beta _{3}q^{6}-2\beta _{1}q^{7}+\cdots\)
2175.2.c.h 2175.c 5.b $4$ $17.367$ \(\Q(i, \sqrt{17})\) None 435.2.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-3+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots\)
2175.2.c.i 2175.c 5.b $4$ $17.367$ \(\Q(\zeta_{8})\) None 2175.2.a.n \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{6}+\zeta_{8}q^{7}+\cdots\)
2175.2.c.j 2175.c 5.b $4$ $17.367$ \(\Q(i, \sqrt{5})\) None 435.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
2175.2.c.k 2175.c 5.b $4$ $17.367$ \(\Q(i, \sqrt{5})\) None 87.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots\)
2175.2.c.l 2175.c 5.b $6$ $17.367$ 6.0.3356224.1 None 87.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+\beta _{3}q^{3}+(-2-\beta _{4}+\cdots)q^{4}+\cdots\)
2175.2.c.m 2175.c 5.b $6$ $17.367$ 6.0.14077504.1 None 435.2.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}-\beta _{5}q^{6}+\cdots\)
2175.2.c.n 2175.c 5.b $8$ $17.367$ 8.0.1267360000.3 None 435.2.a.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{5})q^{2}-\beta _{5}q^{3}+(-2+\beta _{4}+\cdots)q^{4}+\cdots\)
2175.2.c.o 2175.c 5.b $14$ $17.367$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 2175.2.a.ba \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-1+\beta _{2})q^{4}+\beta _{6}q^{6}+\cdots\)
2175.2.c.p 2175.c 5.b $16$ $17.367$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 2175.2.a.bc \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}-\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2175, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2175, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)