Properties

Label 2303.1.d
Level 23032303
Weight 11
Character orbit 2303.d
Rep. character χ2303(2255,)\chi_{2303}(2255,\cdot)
Character field Q\Q
Dimension 1212
Newform subspaces 55
Sturm bound 224224
Trace bound 33

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Defining parameters

Level: N N == 2303=7247 2303 = 7^{2} \cdot 47
Weight: k k == 1 1
Character orbit: [χ][\chi] == 2303.d (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 47 47
Character field: Q\Q
Newform subspaces: 5 5
Sturm bound: 224224
Trace bound: 33

Dimensions

The following table gives the dimensions of various subspaces of M1(2303,[χ])M_{1}(2303, [\chi]).

Total New Old
Modular forms 26 17 9
Cusp forms 18 12 6
Eisenstein series 8 5 3

The following table gives the dimensions of subspaces with specified projective image type.

DnD_n A4A_4 S4S_4 A5A_5
Dimension 12 0 0 0

Trace form

12qq2+q3+11q4+2q62q8+11q92q12+10q16+q178q18q24+12q25+2q278q32+2q34+8q36q372q47q50++q97+O(q100) 12 q - q^{2} + q^{3} + 11 q^{4} + 2 q^{6} - 2 q^{8} + 11 q^{9} - 2 q^{12} + 10 q^{16} + q^{17} - 8 q^{18} - q^{24} + 12 q^{25} + 2 q^{27} - 8 q^{32} + 2 q^{34} + 8 q^{36} - q^{37} - 2 q^{47} - q^{50}+ \cdots + q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S1new(2303,[χ])S_{1}^{\mathrm{new}}(2303, [\chi]) into newform subspaces

Label Char Prim Dim AA Field Image CM RM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
2303.1.d.a 2303.d 47.b 11 1.1491.149 Q\Q D3D_{3} Q(47)\Q(\sqrt{-47}) None 329.1.f.a 1-1 2-2 00 00 qq22q3+2q6+q8+3q9q16+q-q^{2}-2q^{3}+2q^{6}+q^{8}+3q^{9}-q^{16}+\cdots
2303.1.d.b 2303.d 47.b 11 1.1491.149 Q\Q D3D_{3} Q(47)\Q(\sqrt{-47}) None 329.1.f.a 1-1 22 00 00 qq2+2q32q6+q8+3q9q16+q-q^{2}+2q^{3}-2q^{6}+q^{8}+3q^{9}-q^{16}+\cdots
2303.1.d.c 2303.d 47.b 22 1.1491.149 Q(5)\Q(\sqrt{5}) D5D_{5} Q(47)\Q(\sqrt{-47}) None 47.1.b.a 1-1 11 00 00 qβq2+(1β)q3+βq4+q6q8+q-\beta q^{2}+(1-\beta )q^{3}+\beta q^{4}+q^{6}-q^{8}+\cdots
2303.1.d.d 2303.d 47.b 44 1.1491.149 Q(ζ15)+\Q(\zeta_{15})^+ D15D_{15} Q(47)\Q(\sqrt{-47}) None 329.1.f.b 11 2-2 00 00 q+(1β1+β3)q2+β3q3+(1β2+)q4+q+(1-\beta _{1}+\beta _{3})q^{2}+\beta _{3}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots
2303.1.d.e 2303.d 47.b 44 1.1491.149 Q(ζ15)+\Q(\zeta_{15})^+ D15D_{15} Q(47)\Q(\sqrt{-47}) None 329.1.f.b 11 22 00 00 q+(1β1+β3)q2β3q3+(1β2+)q4+q+(1-\beta _{1}+\beta _{3})q^{2}-\beta _{3}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots

Decomposition of S1old(2303,[χ])S_{1}^{\mathrm{old}}(2303, [\chi]) into lower level spaces

S1old(2303,[χ]) S_{1}^{\mathrm{old}}(2303, [\chi]) \simeq S1new(47,[χ])S_{1}^{\mathrm{new}}(47, [\chi])3^{\oplus 3}